Chika Moore - Academia.edu (original) (raw)
Papers by Chika Moore
Japan Journal of Industrial and Applied Mathematics, 2017
In this paper, using Halpern type iteration, we prove a strong convergence theorem for finding a ... more In this paper, using Halpern type iteration, we prove a strong convergence theorem for finding a common element of the set of common fixed points for a finite family of demimetric mappings and the set of common solutions of variational inequality problems for a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems in a Hilbert space.
Computers & Mathematics with Applications, 2001
E be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed va... more E be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed values such that the range of (I-A) is bounded and the inclusion f E Ax has a solution x* E E. It is proved that Ishikawa and Mann type iteration processes converge strongly to x*. Further, if T : E ~-* 2 E is a uniformly continuous and uniformly hemicontractive set-valued map with bounded range and a fixed point x* E E, it is proved that both the Mann and Ishikawa type iteration processes converge strongly to x*. The strong convergence of these iteration processes with errors is also proved. (~
Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consigl... more Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal
The Grants Register 2021, 2020
From the simple beginning of a few scientists gathering to share information to the multifaceted ... more From the simple beginning of a few scientists gathering to share information to the multifaceted organization that exists today, the growth of the AACR reflects the increasing complexity of our understanding of over 200 diseases we now know as cancer.
IOSR Journal of Mathematics, 2017
Journal of Mathematical Analysis and Applications, 1997
We establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to... more We establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to the fixed point of T. Related results deal with the iterative solution of operator equations of the forms f G Tx and f G x + λTx, λ > 0, when T is a set-valued strongly accretive operator. Our theorems include the cases in which the operator T is defined only locally. Explicit error estimates are also given.
Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space ... more Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space H. It is proved that the Ishikawa iteration process converges strongly to a fixed point of T. Furthermore, if T : K i -> H is a continuous pseudocontraction and has a fixed point under this setting, then a modified Ishikawa iteration process converges strongly to a fixed point of T. Finally, as a side but incisive result, it is proved that in uniformly smooth spaces, the duality map is Lipschitz. The method of proof is of independent interest.
Let E be a real p-uniformly smooth Banach space and let A : D(A) c E i-> E be locally Lipschitz a... more Let E be a real p-uniformly smooth Banach space and let A : D(A) c E i-> E be locally Lipschitz and strongly quasi-accretive. It is proved that a Picard recursion process converges strongly to the unique solution of the equation Ax = f, f G R(A) with the convergence being at least as fast as a geometric progression with ratio Ω G (0,1). Related results deal with the convergence of Picard iterations to the fixed point of locally Lipschitz strong hemicontractions and to the solutions of nonlinear equations of the forms x + Tx = f and x-λTx = f where T is an accretive-type operator.
Variational inclusion problems have become the apparatus that is generally used to constrain sund... more Variational inclusion problems have become the apparatus that is generally used to constrain sundry mathematical equations in other to pguarantee the uniqueness and existence of their solutions. The existence of these solutions was earlier studied and proven for uniform Banach Spaces using accretive operators. In this study, we extend the conditions to hold for arbitrary Banach Spaces using uniform accretive operators.
Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space ... more Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space H. It is proved that the Ishikawa iteration process converges strongly to a fixed point of T. Furthermore, if T : K i —> H is a continuous pseudocontraction and has a fixed point under this setting, then a modified Ishikawa iteration process converges strongly to a fixed point of T. Finally, as a side but incisive result, it is proved that in uniformly smooth spaces, the duality map is Lipschitz. The method of proof is of independent interest. MIRAMARE TRIESTE July 1997
Let K be a bounded closed convex nonempty subset of a real uniformly smooth Banach space E. Let T... more Let K be a bounded closed convex nonempty subset of a real uniformly smooth Banach space E. Let T : K i —> K be a strongly pseudocontractive mapping. It is proved that fixed point iteration processes of the Mann and Ishikawa types converge strongly to the fixed point of T and are T-stable. Related results deal with strong convergence and stability of the iteration processes for certain nonlinear operator equations. MIRAMARE TRIESTE July 1997
Let E be an arbitrary real normed linear space and let T : D(T) C E i—> E be locally Lipschitz... more Let E be an arbitrary real normed linear space and let T : D(T) C E i—> E be locally Lipschitzian and locally strongly pseudocontractive with open domain D(T) and a fixed point x* G D(T). It is proved that a Picard recursion process converges strongly to the unique fixed point of T with the convergence being at least as fast as a geometric progression provided the initial guess is taken in some neighbourhood of the fixed point. Related results deal with the convergence of Picard iterations to the solution of the equation Ax = f, where A : D(A) c E —> E is locally strongly accretive and locally Lipschitzian, and to the solutions of nonlinear equations of the forms x + Ax = f and x — λAx = f where A is a locally accretive-type map.
Let E be a real normed linear space and let A : D(A) c E H-* 2£ be a uniformly continuous and uni... more Let E be a real normed linear space and let A : D(A) c E H-* 2£ be a uniformly continuous and unifonnly accretive multivalued map with open domain D(A) such that the inclusion f e Ax has a solution x* e D(A). The strong convergence of iteration processes of the Mann and Ishikawa types to x* is proved. Also preved are related results dealing with the iteration of the fixed point of T, where T : D(T) C E •—* 2E is a uniformly continuous and uniformly pseudocontractive map with an open domain D(T). Furthermore, the strong convergence of these iteration processes with errors is also proved. An example is given to demonstrate that the class of uniformly quasi-accretive (uniformly hemicontractive) maps properly contains the important class of 4>- strongly quasi-accretive (respectively, <£-strongly hemicontractive) maps. Our method of proof is also of independent interest.
IOSR Journal of Mathematics
We established (in our theorem 3.2) a very simple but absolutely very strong and su_cient conditi... more We established (in our theorem 3.2) a very simple but absolutely very strong and su_cient condition for a general weak topology to transmit discreteness property to its range spaces. An immediate consequence of this when applied to product topology (in _nite-or in_nite-dimensions) is that all its range spaces are discrete if a product topology is discrete. Elsewhere we also obtained the conditions for the extension of the coverse: namely, how a discrete range space may induce discreteness on a weak topology.
Mathematical Theory and Modeling, 2013
Let K be a closed convex nonempty subset of a real normed linear space and let T : K i-> K be a L... more Let K be a closed convex nonempty subset of a real normed linear space and let T : K i-> K be a Lipschitz pseudocontraction such that F(T) n K / 0. We introduce the concept of doublesequence iteration processes and prove the strong convergence of such iteration processes to a fixed point of T in K. Related results deal with the strong convergence of the said iteration processes to a solution of the operator equation Ax = f where f G R(A) is an arbitrary but fixed vector and A is an accretive operator mapping E to E.
Japan Journal of Industrial and Applied Mathematics, 2017
In this paper, using Halpern type iteration, we prove a strong convergence theorem for finding a ... more In this paper, using Halpern type iteration, we prove a strong convergence theorem for finding a common element of the set of common fixed points for a finite family of demimetric mappings and the set of common solutions of variational inequality problems for a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems in a Hilbert space.
Computers & Mathematics with Applications, 2001
E be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed va... more E be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed values such that the range of (I-A) is bounded and the inclusion f E Ax has a solution x* E E. It is proved that Ishikawa and Mann type iteration processes converge strongly to x*. Further, if T : E ~-* 2 E is a uniformly continuous and uniformly hemicontractive set-valued map with bounded range and a fixed point x* E E, it is proved that both the Mann and Ishikawa type iteration processes converge strongly to x*. The strong convergence of these iteration processes with errors is also proved. (~
Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consigl... more Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal
The Grants Register 2021, 2020
From the simple beginning of a few scientists gathering to share information to the multifaceted ... more From the simple beginning of a few scientists gathering to share information to the multifaceted organization that exists today, the growth of the AACR reflects the increasing complexity of our understanding of over 200 diseases we now know as cancer.
IOSR Journal of Mathematics, 2017
Journal of Mathematical Analysis and Applications, 1997
We establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to... more We establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to the fixed point of T. Related results deal with the iterative solution of operator equations of the forms f G Tx and f G x + λTx, λ > 0, when T is a set-valued strongly accretive operator. Our theorems include the cases in which the operator T is defined only locally. Explicit error estimates are also given.
Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space ... more Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space H. It is proved that the Ishikawa iteration process converges strongly to a fixed point of T. Furthermore, if T : K i -> H is a continuous pseudocontraction and has a fixed point under this setting, then a modified Ishikawa iteration process converges strongly to a fixed point of T. Finally, as a side but incisive result, it is proved that in uniformly smooth spaces, the duality map is Lipschitz. The method of proof is of independent interest.
Let E be a real p-uniformly smooth Banach space and let A : D(A) c E i-> E be locally Lipschitz a... more Let E be a real p-uniformly smooth Banach space and let A : D(A) c E i-> E be locally Lipschitz and strongly quasi-accretive. It is proved that a Picard recursion process converges strongly to the unique solution of the equation Ax = f, f G R(A) with the convergence being at least as fast as a geometric progression with ratio Ω G (0,1). Related results deal with the convergence of Picard iterations to the fixed point of locally Lipschitz strong hemicontractions and to the solutions of nonlinear equations of the forms x + Tx = f and x-λTx = f where T is an accretive-type operator.
Variational inclusion problems have become the apparatus that is generally used to constrain sund... more Variational inclusion problems have become the apparatus that is generally used to constrain sundry mathematical equations in other to pguarantee the uniqueness and existence of their solutions. The existence of these solutions was earlier studied and proven for uniform Banach Spaces using accretive operators. In this study, we extend the conditions to hold for arbitrary Banach Spaces using uniform accretive operators.
Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space ... more Let T be a continuous pseudocontractive self-map of a compact convex subset K of a Hilbert space H. It is proved that the Ishikawa iteration process converges strongly to a fixed point of T. Furthermore, if T : K i —> H is a continuous pseudocontraction and has a fixed point under this setting, then a modified Ishikawa iteration process converges strongly to a fixed point of T. Finally, as a side but incisive result, it is proved that in uniformly smooth spaces, the duality map is Lipschitz. The method of proof is of independent interest. MIRAMARE TRIESTE July 1997
Let K be a bounded closed convex nonempty subset of a real uniformly smooth Banach space E. Let T... more Let K be a bounded closed convex nonempty subset of a real uniformly smooth Banach space E. Let T : K i —> K be a strongly pseudocontractive mapping. It is proved that fixed point iteration processes of the Mann and Ishikawa types converge strongly to the fixed point of T and are T-stable. Related results deal with strong convergence and stability of the iteration processes for certain nonlinear operator equations. MIRAMARE TRIESTE July 1997
Let E be an arbitrary real normed linear space and let T : D(T) C E i—> E be locally Lipschitz... more Let E be an arbitrary real normed linear space and let T : D(T) C E i—> E be locally Lipschitzian and locally strongly pseudocontractive with open domain D(T) and a fixed point x* G D(T). It is proved that a Picard recursion process converges strongly to the unique fixed point of T with the convergence being at least as fast as a geometric progression provided the initial guess is taken in some neighbourhood of the fixed point. Related results deal with the convergence of Picard iterations to the solution of the equation Ax = f, where A : D(A) c E —> E is locally strongly accretive and locally Lipschitzian, and to the solutions of nonlinear equations of the forms x + Ax = f and x — λAx = f where A is a locally accretive-type map.
Let E be a real normed linear space and let A : D(A) c E H-* 2£ be a uniformly continuous and uni... more Let E be a real normed linear space and let A : D(A) c E H-* 2£ be a uniformly continuous and unifonnly accretive multivalued map with open domain D(A) such that the inclusion f e Ax has a solution x* e D(A). The strong convergence of iteration processes of the Mann and Ishikawa types to x* is proved. Also preved are related results dealing with the iteration of the fixed point of T, where T : D(T) C E •—* 2E is a uniformly continuous and uniformly pseudocontractive map with an open domain D(T). Furthermore, the strong convergence of these iteration processes with errors is also proved. An example is given to demonstrate that the class of uniformly quasi-accretive (uniformly hemicontractive) maps properly contains the important class of 4>- strongly quasi-accretive (respectively, <£-strongly hemicontractive) maps. Our method of proof is also of independent interest.
IOSR Journal of Mathematics
We established (in our theorem 3.2) a very simple but absolutely very strong and su_cient conditi... more We established (in our theorem 3.2) a very simple but absolutely very strong and su_cient condition for a general weak topology to transmit discreteness property to its range spaces. An immediate consequence of this when applied to product topology (in _nite-or in_nite-dimensions) is that all its range spaces are discrete if a product topology is discrete. Elsewhere we also obtained the conditions for the extension of the coverse: namely, how a discrete range space may induce discreteness on a weak topology.
Mathematical Theory and Modeling, 2013
Let K be a closed convex nonempty subset of a real normed linear space and let T : K i-> K be a L... more Let K be a closed convex nonempty subset of a real normed linear space and let T : K i-> K be a Lipschitz pseudocontraction such that F(T) n K / 0. We introduce the concept of doublesequence iteration processes and prove the strong convergence of such iteration processes to a fixed point of T in K. Related results deal with the strong convergence of the said iteration processes to a solution of the operator equation Ax = f where f G R(A) is an arbitrary but fixed vector and A is an accretive operator mapping E to E.