Sahar Mohamed Ali Abou Bakr | Ain Shams University (original) (raw)
Papers by Sahar Mohamed Ali Abou Bakr
Towards coupled coincidence theorems of generalized admissible types of mappings on partial satisfactory cone metric spaces and some applications
This paper introduces a novel class of generalized α-admissible contraction types of mappings in ... more This paper introduces a novel class of generalized α-admissible contraction types of mappings in the framework of θ-complete partial satisfactory cone metric spaces and proves the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.
Fixed point theorems of generalized contraction mappings on ϖ-cone metric spaces over Banach algebras
Without the assumptions of normality and solidness, we investigate some properties of cones with ... more Without the assumptions of normality and solidness, we investigate some properties of cones with some semiinterior points in normed algebras, introduce two novel notions of S-set and S-number associated with every semiinterior point in the underlying cone, give a constructive example with calculations of these new quantities, study some topological characterization of the topology induced by ϖ-cone metric of ϖ-cone metric space over Banach algebra with the help of semiinterior points instead of interior points, and then generalize some fixed point theorems of contraction type mapping defined on ϖ-cone metric space over Banach algebra with nonnormal and nonsolid cone. 2020 AMS Mathematics subject classification: primary 47H09; secondary 47H10.
Journal of Inequalities and Applications
In this paper, we introduce some user-friendly versions of integral-type fixed-point results and ... more In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1E1_{E}1E 1 E -complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature.
In this paper, we study some facts concerning the topological structures of some subsets of a giv... more In this paper, we study some facts concerning the topological structures of some subsets of a given normed space, prove the existence of a unique fixed point of rrr-contraction mappings defined on cartesian product of a closed and weakly Cauchy subset of a weakly complete normed space, propose an iterated sequence that converges strongly to such a unique fixed point, and prove the existence of fixed points of nonexpansive mapping defined on cartesian product of a closed and sequentially Cauchy subset of a weakly complete normed space.
Journal of Mathematics and Statistics
New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ... more New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ-φ-contraction types of mapping are defined and the existence of fixed point for such types has been proved. These results mainly generalize fixed point theorems in some previous research papers.
Journal of Mathematics
This paper introduces the concept of the theta cone metric, studies its various topological prope... more This paper introduces the concept of the theta cone metric, studies its various topological properties, and gives some examples of it. Furthermore, it proves some lemmas and then uses them to give further generalizations of some well-known fixed point theorems. Specifically, Theorem 2 of the paper is a generalization of Reich’s fixed point theorem.
Journal of Mathematics, 2021
This paper proves the existence of a unique coupled fixed point of some type of contraction mappi... more This paper proves the existence of a unique coupled fixed point of some type of contraction mappings defined on a complete - cone and - theta cone metric spaces; consequently, it extends and generalizes many previous coupled fixed point theorems.
Abstract and Applied Analysis, 2021
This paper introduces novel concepts of joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak contraction and... more This paper introduces novel concepts of joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak contraction and joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G‐ΩS,ðabef Þ-weak contraction and cyclic G‐ΩS,ðabef Þ-weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic ΩS,ðabef Þ-weak contraction and cyclic ΩS,ðabef Þ-weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.
Journal of Mathematics, 2020
This paper introduces the concept of the theta cone metric, studies its various topological prope... more This paper introduces the concept of the theta cone metric, studies its various topological properties, and gives some examples of it. Furthermore, it proves some lemmas and then uses them to give further generalizations of some well-known fixed point theorems. Specifically, Theorem 2 of the paper is a generalization of Reich’s fixed point theorem.
This textbook is written to develop thorough understanding the mastery behind the foundations of ... more This textbook is written to develop thorough understanding the mastery behind the foundations of geometry that needed to solve geometric problems using vectors in three dimensional Euclidean space at a useful proficiency level, it introduces a comprehensive study on three dimensional Euclidean spaces’ objects, namely; points, line segments, vectors, straight lines, planes, spheres, cylinders, quadratic surfaces in general analytically, and includes different comparisons between such studied objects among themselves, it focuses on the orthogonal projections of a point and directed line segment on line, on plane, and on sphere, and it is recommended world widely for the second level universities’ students, its contents are written in a systematic, streaming, understandable and attractive way for student’s interest, supported with adequate number of examples, exercises, problem solving and applications to meet the quality standard. Moreover; it is a prerequisite for some other fields o...
The topics of this textbook are curves in differential geometry and they are primarily studied by... more The topics of this textbook are curves in differential geometry and they are primarily studied by means of parametrization. Particularly; curvilinear coordinates, plane curves and skew curves like; helices, involutes, evolutes, spherical indicatrix, circles and spheres of curvatures. It also introduces some quadratic surfaces, theory of contacts, curves-surfaces contacts relationships, envelops, the geometry of curves in differential geometry in general. The main properties of these objects, which will be studied, are notions related to the shape;tangents, principle normals, binormals,tangent lines, normal planes, osculating planes, and rectifying planes. The fundamental investigated concepts are curvatures and torsion as the basic intrinsic property of a curve, independent of its isometric embedding in Euclidean space. One of the most important tools used to analyze a curve is the Serret-Frenet frame,a moving frame that provides a coordinate system at each point of the curve that i...
International Journal of Mathematics and Statistics, 2017
This paper suggests new cyclic weak contraction type of mapping and proves the existence of a uni... more This paper suggests new cyclic weak contraction type of mapping and proves the existence of a unique fixed point for such a type. The result of this paper generalizes the fixed point theorem proved in some previous research paper.
Journal of Mathematics and Statistics, Apr 1, 2017
New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ... more New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ-φ-contraction types of mapping are defined and the existence of fixed point for such types has been proved. These results mainly generalize fixed point theorems in some previous research papers.
This manuscript proves the existence of a single common fixed point of two joint ðA, BÞ generaliz... more This manuscript proves the existence of a single common fixed point of two joint ðA, BÞ generalized cyclic φ − abc weak nonexpansive mappings, where A and B are compact sets. The result in particular demonstrated a single fixed point of generalized cyclic φ − abc weak nonexpansive mappings, without the assumption of a single contracting point. Additionally, it introduces new types of generalized cyclic abc ; r contraction mappings and describes the existence of a single fixed point of them in b-metric spaces. Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic abc ; r contraction mappings, extend, and generalize some of the previous reported results.
Journal of Mathematics and Statistics, 2007
We defined new concept of complete sequences of equivalence relations on a given abstract set on ... more We defined new concept of complete sequences of equivalence relations on a given abstract set on which no topology is considered, the concept of contraction mappings with respect to these sequences, proved the existence of a fixed point of a multivalued and in particular single valued mappings T on the given abstract set.
Applied Mathematics and Computation, 2004
In this paper we study the projections and some recovery problem of a finite codimensional Banach... more In this paper we study the projections and some recovery problem of a finite codimensional Banach spaces in terms of the projection of their complementations, more precisely we study the following problems: (1) If Y is a finite co-dimensional subspace of a Banach space X and Z is its complementation, is for every projection P 0 from X onto Z and every > 0 there a projection P from X onto Y satisfying kP k 6 1 þ ð1 þ ÞkP 0 k? (2) If X is a Banach space, x 2 X , Y is an n-co-dimensional subspace of X and (ff i ; x i g n i¼1) is the Auerbach system of the complementation Z of Y in X , is there an element y 2 Y satisfying the following two conditions (i)f i ðyÞ ¼f i ðxÞ 8i 2 f1; 2;. .. ; ng, wheref i is the Hahn-Banach extension of f i on X , (ii) kyk 6 Mkxk for some constant M? And we study the restrictions placed on the constant M as a function of X and Y .
Abstract and Applied Analysis, 2001
We give the sufficient conditions for the existence of a metric projection onto convex closed sub... more We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spacesl p,1≤p<∞andc 0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator froml p,1≤p<∞orc 0onto anyone of their maximal proper subspaces.
Abstract and Applied Analysis, 2001
We find a lower estimation for the projection constant of the projective tensor productX⊗ ∧Yand t... more We find a lower estimation for the projection constant of the projective tensor productX⊗ ∧Yand the injective tensor productX⊗ ∨Y, we apply this estimation on some previous results, and we also introduce a new concept of the projection constants of operators rather than that defined for Banach spaces.
Journal of Mathematics and Statistics, 2007
We showed that the generalized contraction mapping defined on a closed convex subset of a weakly ... more We showed that the generalized contraction mapping defined on a closed convex subset of a weakly Cauchy normed space has a unique fixed point. Moreover, the sequence of iterates of any element in the domain of the given mapping is converging strongly to the fixed point of such a mapping.
Journal of Mathematics
This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifi... more This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifically, Theorem 3 of the paper is the generalization of the Baskar–Lackshmikantham coupled fixed-point theorem, and Theorem 5 is the generalization of the Sahar Mohamed Ali Abou Bakr fixed-point theorem, where the underlying space is complete θ -cone-metric space.
Towards coupled coincidence theorems of generalized admissible types of mappings on partial satisfactory cone metric spaces and some applications
This paper introduces a novel class of generalized α-admissible contraction types of mappings in ... more This paper introduces a novel class of generalized α-admissible contraction types of mappings in the framework of θ-complete partial satisfactory cone metric spaces and proves the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.
Fixed point theorems of generalized contraction mappings on ϖ-cone metric spaces over Banach algebras
Without the assumptions of normality and solidness, we investigate some properties of cones with ... more Without the assumptions of normality and solidness, we investigate some properties of cones with some semiinterior points in normed algebras, introduce two novel notions of S-set and S-number associated with every semiinterior point in the underlying cone, give a constructive example with calculations of these new quantities, study some topological characterization of the topology induced by ϖ-cone metric of ϖ-cone metric space over Banach algebra with the help of semiinterior points instead of interior points, and then generalize some fixed point theorems of contraction type mapping defined on ϖ-cone metric space over Banach algebra with nonnormal and nonsolid cone. 2020 AMS Mathematics subject classification: primary 47H09; secondary 47H10.
Journal of Inequalities and Applications
In this paper, we introduce some user-friendly versions of integral-type fixed-point results and ... more In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1E1_{E}1E 1 E -complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature.
In this paper, we study some facts concerning the topological structures of some subsets of a giv... more In this paper, we study some facts concerning the topological structures of some subsets of a given normed space, prove the existence of a unique fixed point of rrr-contraction mappings defined on cartesian product of a closed and weakly Cauchy subset of a weakly complete normed space, propose an iterated sequence that converges strongly to such a unique fixed point, and prove the existence of fixed points of nonexpansive mapping defined on cartesian product of a closed and sequentially Cauchy subset of a weakly complete normed space.
Journal of Mathematics and Statistics
New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ... more New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ-φ-contraction types of mapping are defined and the existence of fixed point for such types has been proved. These results mainly generalize fixed point theorems in some previous research papers.
Journal of Mathematics
This paper introduces the concept of the theta cone metric, studies its various topological prope... more This paper introduces the concept of the theta cone metric, studies its various topological properties, and gives some examples of it. Furthermore, it proves some lemmas and then uses them to give further generalizations of some well-known fixed point theorems. Specifically, Theorem 2 of the paper is a generalization of Reich’s fixed point theorem.
Journal of Mathematics, 2021
This paper proves the existence of a unique coupled fixed point of some type of contraction mappi... more This paper proves the existence of a unique coupled fixed point of some type of contraction mappings defined on a complete - cone and - theta cone metric spaces; consequently, it extends and generalizes many previous coupled fixed point theorems.
Abstract and Applied Analysis, 2021
This paper introduces novel concepts of joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak contraction and... more This paper introduces novel concepts of joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak contraction and joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G‐ΩS,ðabef Þ-weak contraction and cyclic G‐ΩS,ðabef Þ-weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic ΩS,ðabef Þ-weak contraction and cyclic ΩS,ðabef Þ-weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.
Journal of Mathematics, 2020
This paper introduces the concept of the theta cone metric, studies its various topological prope... more This paper introduces the concept of the theta cone metric, studies its various topological properties, and gives some examples of it. Furthermore, it proves some lemmas and then uses them to give further generalizations of some well-known fixed point theorems. Specifically, Theorem 2 of the paper is a generalization of Reich’s fixed point theorem.
This textbook is written to develop thorough understanding the mastery behind the foundations of ... more This textbook is written to develop thorough understanding the mastery behind the foundations of geometry that needed to solve geometric problems using vectors in three dimensional Euclidean space at a useful proficiency level, it introduces a comprehensive study on three dimensional Euclidean spaces’ objects, namely; points, line segments, vectors, straight lines, planes, spheres, cylinders, quadratic surfaces in general analytically, and includes different comparisons between such studied objects among themselves, it focuses on the orthogonal projections of a point and directed line segment on line, on plane, and on sphere, and it is recommended world widely for the second level universities’ students, its contents are written in a systematic, streaming, understandable and attractive way for student’s interest, supported with adequate number of examples, exercises, problem solving and applications to meet the quality standard. Moreover; it is a prerequisite for some other fields o...
The topics of this textbook are curves in differential geometry and they are primarily studied by... more The topics of this textbook are curves in differential geometry and they are primarily studied by means of parametrization. Particularly; curvilinear coordinates, plane curves and skew curves like; helices, involutes, evolutes, spherical indicatrix, circles and spheres of curvatures. It also introduces some quadratic surfaces, theory of contacts, curves-surfaces contacts relationships, envelops, the geometry of curves in differential geometry in general. The main properties of these objects, which will be studied, are notions related to the shape;tangents, principle normals, binormals,tangent lines, normal planes, osculating planes, and rectifying planes. The fundamental investigated concepts are curvatures and torsion as the basic intrinsic property of a curve, independent of its isometric embedding in Euclidean space. One of the most important tools used to analyze a curve is the Serret-Frenet frame,a moving frame that provides a coordinate system at each point of the curve that i...
International Journal of Mathematics and Statistics, 2017
This paper suggests new cyclic weak contraction type of mapping and proves the existence of a uni... more This paper suggests new cyclic weak contraction type of mapping and proves the existence of a unique fixed point for such a type. The result of this paper generalizes the fixed point theorem proved in some previous research paper.
Journal of Mathematics and Statistics, Apr 1, 2017
New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ... more New B-U-cyclic weak contraction C-class function concept has been introduced, B-U-cyclic weak F-φ-φ-contraction types of mapping are defined and the existence of fixed point for such types has been proved. These results mainly generalize fixed point theorems in some previous research papers.
This manuscript proves the existence of a single common fixed point of two joint ðA, BÞ generaliz... more This manuscript proves the existence of a single common fixed point of two joint ðA, BÞ generalized cyclic φ − abc weak nonexpansive mappings, where A and B are compact sets. The result in particular demonstrated a single fixed point of generalized cyclic φ − abc weak nonexpansive mappings, without the assumption of a single contracting point. Additionally, it introduces new types of generalized cyclic abc ; r contraction mappings and describes the existence of a single fixed point of them in b-metric spaces. Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic abc ; r contraction mappings, extend, and generalize some of the previous reported results.
Journal of Mathematics and Statistics, 2007
We defined new concept of complete sequences of equivalence relations on a given abstract set on ... more We defined new concept of complete sequences of equivalence relations on a given abstract set on which no topology is considered, the concept of contraction mappings with respect to these sequences, proved the existence of a fixed point of a multivalued and in particular single valued mappings T on the given abstract set.
Applied Mathematics and Computation, 2004
In this paper we study the projections and some recovery problem of a finite codimensional Banach... more In this paper we study the projections and some recovery problem of a finite codimensional Banach spaces in terms of the projection of their complementations, more precisely we study the following problems: (1) If Y is a finite co-dimensional subspace of a Banach space X and Z is its complementation, is for every projection P 0 from X onto Z and every > 0 there a projection P from X onto Y satisfying kP k 6 1 þ ð1 þ ÞkP 0 k? (2) If X is a Banach space, x 2 X , Y is an n-co-dimensional subspace of X and (ff i ; x i g n i¼1) is the Auerbach system of the complementation Z of Y in X , is there an element y 2 Y satisfying the following two conditions (i)f i ðyÞ ¼f i ðxÞ 8i 2 f1; 2;. .. ; ng, wheref i is the Hahn-Banach extension of f i on X , (ii) kyk 6 Mkxk for some constant M? And we study the restrictions placed on the constant M as a function of X and Y .
Abstract and Applied Analysis, 2001
We give the sufficient conditions for the existence of a metric projection onto convex closed sub... more We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spacesl p,1≤p<∞andc 0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator froml p,1≤p<∞orc 0onto anyone of their maximal proper subspaces.
Abstract and Applied Analysis, 2001
We find a lower estimation for the projection constant of the projective tensor productX⊗ ∧Yand t... more We find a lower estimation for the projection constant of the projective tensor productX⊗ ∧Yand the injective tensor productX⊗ ∨Y, we apply this estimation on some previous results, and we also introduce a new concept of the projection constants of operators rather than that defined for Banach spaces.
Journal of Mathematics and Statistics, 2007
We showed that the generalized contraction mapping defined on a closed convex subset of a weakly ... more We showed that the generalized contraction mapping defined on a closed convex subset of a weakly Cauchy normed space has a unique fixed point. Moreover, the sequence of iterates of any element in the domain of the given mapping is converging strongly to the fixed point of such a mapping.
Journal of Mathematics
This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifi... more This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifically, Theorem 3 of the paper is the generalization of the Baskar–Lackshmikantham coupled fixed-point theorem, and Theorem 5 is the generalization of the Sahar Mohamed Ali Abou Bakr fixed-point theorem, where the underlying space is complete θ -cone-metric space.