Memudu Olatinwo - Academia.edu (original) (raw)

Papers by Memudu Olatinwo

Fasciculi Mathematici, 2008

... Amer. Math. Soc., 44(1953), 506-510. [14] Noor MA, Three-Step Iterative Algorithms for Multiv... more ... Amer. Math. Soc., 44(1953), 506-510. [14] Noor MA, Three-Step Iterative Algorithms for Multivalued Quasi Varia-tional Inclusions, J. Math. Anal. ... [22] SL Singh SL, Bhatnagar C., Mishra SN, Stability of Jungck-Type It-erative Procedures, International J. Math. & Math. ...

arXiv (Cornell University), Dec 15, 2019

Fenyves BCI-algebras are BCI-algebras that satisfy the Bol-Moufang identities. In this paper, the... more Fenyves BCI-algebras are BCI-algebras that satisfy the Bol-Moufang identities. In this paper, the holomorphy of BCI-algebras are studied. It is shown that whenever a loop and its holomorph are BCI-algebras, the former is psemisimple if and only if the latter is p-semisimple. Whenever a loop and its holomorph are BCI-algebras, it is established that the former is a BCK-algebra if and only if the latter has a BCKsubalgebra. Moreover, the holomorphy of the associative and some non-associative Fenyves BCI-algebras are also studied.

In this paper, we shall establish error estimates for two important flxed point theorems involvin... more In this paper, we shall establish error estimates for two important flxed point theorems involving contractive conditions of integral type. Apart from obtaining the error estimates and the rate of convergence for a recent result of Rhoades [18] by imposing an additional condition, a generalization of Berinde [4] is also established in Theorem 2 by introducing a weak contraction condition of integral type in the present paper. Our results are generalizations and extensions of several well-known results as contained in the reference section of this paper. In particular, our results generalize, extend and improve corresponding results in [4, 5, 6, 8]. 2000 Mathematics Subject Classiflcation: 47H06, 54H25.

In this paper, we examine the stability of KirkIshikawa and Kirk-Mann iteration processes for non... more In this paper, we examine the stability of KirkIshikawa and Kirk-Mann iteration processes for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space. To the best of our knowledge, apart from the results of Olatinwo [19], stability of fixed point iteration processes has not been investigated in uniformly convex Banach space. Our results generalize, extend and improve some of the results of Harder and Hicks [11], Rhoades [26, 27], Osilike [23], Berinde [2, 3] as well as Imoru and Olatinwo [12].

Creative Mathematics and Informatics, 2012

In this paper, we obtain some fixed point theorems for more general classes of mappings than the ... more In this paper, we obtain some fixed point theorems for more general classes of mappings than the A−contractions of Akram et al. We also give an example of mappings satisfying our new class of contractive mappings but which does not satisfy the contractive condition of Akram et al. Our results generalize and extend the recent results of Akram et al., and unify several other classical results in the literature.

JP Journal of Fixed Point Theory and Applications, 2017

In this paper, we establish some common fixed point theorems for selfmappings in uniform space by... more In this paper, we establish some common fixed point theorems for selfmappings in uniform space by employing both the concepts of an A−distance and an E−distance introduced by Aamri and El Moutawakil [1]. We employ a contractive definition independent of those of Olatinwo [8] and Aamri and El Moutawakil [1]. Our results are also independent of those of Olatinwo [8] as well as independent of Theorems 3.1-3.3 of Aamri and El Moutawakil [1].

Matematicki Vesnik

In this paper, we prove some stability results for two newly introduced hybrid fixed point iterat... more In this paper, we prove some stability results for two newly introduced hybrid fixed point iterative algorithms of Kirk-Ishikawa and Kirk-Mann Type in normed linear space using a certain contractive condition. Our results generalize, extend and improve some of the results of Harder and Hicks [11], Rhoades [29,30], Osilike [26], Berinde [2,3] as well as the recent results of the author [12,23,24,25].

Central European Journal of Mathematics, 2008

In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Pi... more In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete −metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results also improve the recent results of Daffer and Kaneko [16].

Abstract and Applied Analysis, 2010

Some results of (Ćirić, 1974) on a nonunique fixed point theorem on the class of metric spaces ar... more Some results of (Ćirić, 1974) on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.

In this paper, we establish some convergence results in a complete b−metric space for the Picard ... more In this paper, we establish some convergence results in a complete b−metric space for the Picard iteration associated to two multi-valued weak contractions by employing the concepts of monotone and comparison functions. Our results generalize and extend those of Berinde and Berinde [8], Daffer and Kaneko [15] and Nadler [27]. Theorem 2.1 in our paper generalizes Theorem 5 of Nadler [27] and a recent result of Berinde and Berinde [8], it also extends, improves and unifies several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Also, Theorem 2.3 is a generalization and extension of Theorem 5 of Nadler [27] as well as Theorem 4 of Berinde and Berinde [8].

Banach in 1922 proved the celebrated result which is well-known in the literature as the Banach&#... more Banach in 1922 proved the celebrated result which is well-known in the literature as the Banach's Fixed Point Theorem or the Con- traction Mapping Principle. This result of Banach also known as the Theorem of Picard-Banach-Cacciopoli is contained in several mono- graphs including Agarwal et al (1), Berinde (3, 4, 5) and Zeidler (17). In this paper, we shall establish the error estimates as well as the rate of convergence for a version of the Banach's Fixed Point The- orem by employing a certain form of '¡contraction different from that of Berinde (5). Our results are generalizations of those of Banach (2) and Berinde (3, 4, 5)

Abstract. In this paper, we establish some common fixed point theorems for selfmappings in unifor... more Abstract. In this paper, we establish some common fixed point theorems for selfmappings in uniform spaces by employing the concepts of an A-distance, an E-distance as well as the notion of comparison function. A more general contractive condition than that used to establish some of the results of Aamri and El Moutawakil [1] is employed to obtain our results. Our results are generalizations of some of the results of [1]. 1.

In this paper, we establish some strong convergence results for Mann and Ishikawa iterative proce... more In this paper, we establish some strong convergence results for Mann and Ishikawa iterative processes in a Banach space setting by employing some general contractive conditions as well as weakening further the conditions on the parameter sequence { n} ⊂ [0, 1]. In addition, in some of our results, we introduce some innovative ideas which make our results distinct from some previous ones. In particular, our results generalize, extend and improve those of [V. Berinde; On the convergence of Mann iteration for a class of quasicontractive operators, Preprint, North University of Baia Mare (2003)] and [V. Berinde; On the Convergence of the Ishikawa Iteration in the Class of Quasi-contractive Operators, Acta Math. Univ. Comenianae Vol. LXXIII (1) (2004), 119-126] as well as some other analogous results in the literature.

In this paper, we shall establish error estimates for two important fixed point theorems involvin... more In this paper, we shall establish error estimates for two important fixed point theorems involving contractive conditions of integral type. Apart from obtaining the error estimates and the rate of convergence for a recent result of Rhoades [18] by imposing an additional condition, a generalization of Berinde [4] is also established in Theorem 2 by introducing a weak contraction condition of integral type in the present paper. Our results are generalizations and extensions of several well-known results as contained in the reference section of this paper. In particular, our results generalize, extend and improve corresponding results in [4, 5, 6, 8]. 2000 Mathematics Subject Classification: 47H06, 54H25.

Adeagbo-Sheikh [1] gave the detail about the notions of the 'distance function (g(t)) and the 'wo... more Adeagbo-Sheikh [1] gave the detail about the notions of the 'distance function (g(t)) and the 'working functions (y * i (t), i = 1, 2, ..., n). The working functions are the functions which describe the behaviours of the subsystems during self-organization process. The procedure for obtaining these working functions for a system of three particles which is self-organizing to keep the particles in a straight line was discussed in Olatinwo and Adeagbo-Sheikh[4]. In this paper, we employ some concepts of the probability theory, elementary properties of curve as well as the distance function to determine the degree of progress to goal at any stage during self-organization process. We consider the probability of reaching the goal at any stage of the self-organization process as its degree of process to goal during this process. The results obtained are in agreement with the axiomatic properties of probability.

In the paper [M. O. Olatinwo, Stability of coupled fixed point iterations and the continuous depe... more In the paper [M. O. Olatinwo, Stability of coupled fixed point iterations and the continuous dependence of coupled fixed points, Communications on Applied Nonlinear Analysis 19 (2012), 71-83], the author has extended the notion of stability of fixed point iterative procedures contained in the paper [A. M. Harder and T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japonica 33 (1988), 693-706], as well as the continuous dependence of fixed points to the coupled fixed point settings by employing the contractive conditions and the coupled fixed point iteration in the article [F. Sabetghadam, H. P. Masiha and A. H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory and Applications, Article ID 125426 (2009)]. In the present paper, we obtain some results on stability of coupled fixed point iterative procedures by using rational type contractive conditions.

In this paper, we obtain some stability results in complete convex metric spaces for selfmappings... more In this paper, we obtain some stability results in complete convex metric spaces for selfmappings satisfying certain general contractivity conditions. Our results extend several stability results in the literature. AMS CLASSIFICATION NUMBERS: 47H06, 54H25.

In this paper, we establish some common fixed point theorems for selfmappings in uniform spaces b... more In this paper, we establish some common fixed point theorems for selfmappings in uniform spaces by employing the concepts of an A-distance and an E-distance introduced by Aamri and El Moutawakil [3] as well as the notion of comparison functions. We employ a more general contractive definition than that of Aamri and El Moutawakil [3]. Our results are generalizations of Theorems 3.1-3.3 of [3] and those of Olatinwo [12, 13].

Fasciculi Mathematici, 2008

... Amer. Math. Soc., 44(1953), 506-510. [14] Noor MA, Three-Step Iterative Algorithms for Multiv... more ... Amer. Math. Soc., 44(1953), 506-510. [14] Noor MA, Three-Step Iterative Algorithms for Multivalued Quasi Varia-tional Inclusions, J. Math. Anal. ... [22] SL Singh SL, Bhatnagar C., Mishra SN, Stability of Jungck-Type It-erative Procedures, International J. Math. & Math. ...

arXiv (Cornell University), Dec 15, 2019

Fenyves BCI-algebras are BCI-algebras that satisfy the Bol-Moufang identities. In this paper, the... more Fenyves BCI-algebras are BCI-algebras that satisfy the Bol-Moufang identities. In this paper, the holomorphy of BCI-algebras are studied. It is shown that whenever a loop and its holomorph are BCI-algebras, the former is psemisimple if and only if the latter is p-semisimple. Whenever a loop and its holomorph are BCI-algebras, it is established that the former is a BCK-algebra if and only if the latter has a BCKsubalgebra. Moreover, the holomorphy of the associative and some non-associative Fenyves BCI-algebras are also studied.

In this paper, we shall establish error estimates for two important flxed point theorems involvin... more In this paper, we shall establish error estimates for two important flxed point theorems involving contractive conditions of integral type. Apart from obtaining the error estimates and the rate of convergence for a recent result of Rhoades [18] by imposing an additional condition, a generalization of Berinde [4] is also established in Theorem 2 by introducing a weak contraction condition of integral type in the present paper. Our results are generalizations and extensions of several well-known results as contained in the reference section of this paper. In particular, our results generalize, extend and improve corresponding results in [4, 5, 6, 8]. 2000 Mathematics Subject Classiflcation: 47H06, 54H25.

In this paper, we examine the stability of KirkIshikawa and Kirk-Mann iteration processes for non... more In this paper, we examine the stability of KirkIshikawa and Kirk-Mann iteration processes for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space. To the best of our knowledge, apart from the results of Olatinwo [19], stability of fixed point iteration processes has not been investigated in uniformly convex Banach space. Our results generalize, extend and improve some of the results of Harder and Hicks [11], Rhoades [26, 27], Osilike [23], Berinde [2, 3] as well as Imoru and Olatinwo [12].

Creative Mathematics and Informatics, 2012

In this paper, we obtain some fixed point theorems for more general classes of mappings than the ... more In this paper, we obtain some fixed point theorems for more general classes of mappings than the A−contractions of Akram et al. We also give an example of mappings satisfying our new class of contractive mappings but which does not satisfy the contractive condition of Akram et al. Our results generalize and extend the recent results of Akram et al., and unify several other classical results in the literature.

JP Journal of Fixed Point Theory and Applications, 2017

In this paper, we establish some common fixed point theorems for selfmappings in uniform space by... more In this paper, we establish some common fixed point theorems for selfmappings in uniform space by employing both the concepts of an A−distance and an E−distance introduced by Aamri and El Moutawakil [1]. We employ a contractive definition independent of those of Olatinwo [8] and Aamri and El Moutawakil [1]. Our results are also independent of those of Olatinwo [8] as well as independent of Theorems 3.1-3.3 of Aamri and El Moutawakil [1].

Matematicki Vesnik

In this paper, we prove some stability results for two newly introduced hybrid fixed point iterat... more In this paper, we prove some stability results for two newly introduced hybrid fixed point iterative algorithms of Kirk-Ishikawa and Kirk-Mann Type in normed linear space using a certain contractive condition. Our results generalize, extend and improve some of the results of Harder and Hicks [11], Rhoades [29,30], Osilike [26], Berinde [2,3] as well as the recent results of the author [12,23,24,25].

Central European Journal of Mathematics, 2008

In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Pi... more In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete −metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results also improve the recent results of Daffer and Kaneko [16].

Abstract and Applied Analysis, 2010

Some results of (Ćirić, 1974) on a nonunique fixed point theorem on the class of metric spaces ar... more Some results of (Ćirić, 1974) on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.

In this paper, we establish some convergence results in a complete b−metric space for the Picard ... more In this paper, we establish some convergence results in a complete b−metric space for the Picard iteration associated to two multi-valued weak contractions by employing the concepts of monotone and comparison functions. Our results generalize and extend those of Berinde and Berinde [8], Daffer and Kaneko [15] and Nadler [27]. Theorem 2.1 in our paper generalizes Theorem 5 of Nadler [27] and a recent result of Berinde and Berinde [8], it also extends, improves and unifies several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Also, Theorem 2.3 is a generalization and extension of Theorem 5 of Nadler [27] as well as Theorem 4 of Berinde and Berinde [8].

Banach in 1922 proved the celebrated result which is well-known in the literature as the Banach&#... more Banach in 1922 proved the celebrated result which is well-known in the literature as the Banach's Fixed Point Theorem or the Con- traction Mapping Principle. This result of Banach also known as the Theorem of Picard-Banach-Cacciopoli is contained in several mono- graphs including Agarwal et al (1), Berinde (3, 4, 5) and Zeidler (17). In this paper, we shall establish the error estimates as well as the rate of convergence for a version of the Banach's Fixed Point The- orem by employing a certain form of '¡contraction different from that of Berinde (5). Our results are generalizations of those of Banach (2) and Berinde (3, 4, 5)

Abstract. In this paper, we establish some common fixed point theorems for selfmappings in unifor... more Abstract. In this paper, we establish some common fixed point theorems for selfmappings in uniform spaces by employing the concepts of an A-distance, an E-distance as well as the notion of comparison function. A more general contractive condition than that used to establish some of the results of Aamri and El Moutawakil [1] is employed to obtain our results. Our results are generalizations of some of the results of [1]. 1.

In this paper, we establish some strong convergence results for Mann and Ishikawa iterative proce... more In this paper, we establish some strong convergence results for Mann and Ishikawa iterative processes in a Banach space setting by employing some general contractive conditions as well as weakening further the conditions on the parameter sequence { n} ⊂ [0, 1]. In addition, in some of our results, we introduce some innovative ideas which make our results distinct from some previous ones. In particular, our results generalize, extend and improve those of [V. Berinde; On the convergence of Mann iteration for a class of quasicontractive operators, Preprint, North University of Baia Mare (2003)] and [V. Berinde; On the Convergence of the Ishikawa Iteration in the Class of Quasi-contractive Operators, Acta Math. Univ. Comenianae Vol. LXXIII (1) (2004), 119-126] as well as some other analogous results in the literature.

In this paper, we shall establish error estimates for two important fixed point theorems involvin... more In this paper, we shall establish error estimates for two important fixed point theorems involving contractive conditions of integral type. Apart from obtaining the error estimates and the rate of convergence for a recent result of Rhoades [18] by imposing an additional condition, a generalization of Berinde [4] is also established in Theorem 2 by introducing a weak contraction condition of integral type in the present paper. Our results are generalizations and extensions of several well-known results as contained in the reference section of this paper. In particular, our results generalize, extend and improve corresponding results in [4, 5, 6, 8]. 2000 Mathematics Subject Classification: 47H06, 54H25.

Adeagbo-Sheikh [1] gave the detail about the notions of the 'distance function (g(t)) and the 'wo... more Adeagbo-Sheikh [1] gave the detail about the notions of the 'distance function (g(t)) and the 'working functions (y * i (t), i = 1, 2, ..., n). The working functions are the functions which describe the behaviours of the subsystems during self-organization process. The procedure for obtaining these working functions for a system of three particles which is self-organizing to keep the particles in a straight line was discussed in Olatinwo and Adeagbo-Sheikh[4]. In this paper, we employ some concepts of the probability theory, elementary properties of curve as well as the distance function to determine the degree of progress to goal at any stage during self-organization process. We consider the probability of reaching the goal at any stage of the self-organization process as its degree of process to goal during this process. The results obtained are in agreement with the axiomatic properties of probability.

In the paper [M. O. Olatinwo, Stability of coupled fixed point iterations and the continuous depe... more In the paper [M. O. Olatinwo, Stability of coupled fixed point iterations and the continuous dependence of coupled fixed points, Communications on Applied Nonlinear Analysis 19 (2012), 71-83], the author has extended the notion of stability of fixed point iterative procedures contained in the paper [A. M. Harder and T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japonica 33 (1988), 693-706], as well as the continuous dependence of fixed points to the coupled fixed point settings by employing the contractive conditions and the coupled fixed point iteration in the article [F. Sabetghadam, H. P. Masiha and A. H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory and Applications, Article ID 125426 (2009)]. In the present paper, we obtain some results on stability of coupled fixed point iterative procedures by using rational type contractive conditions.

In this paper, we obtain some stability results in complete convex metric spaces for selfmappings... more In this paper, we obtain some stability results in complete convex metric spaces for selfmappings satisfying certain general contractivity conditions. Our results extend several stability results in the literature. AMS CLASSIFICATION NUMBERS: 47H06, 54H25.

In this paper, we establish some common fixed point theorems for selfmappings in uniform spaces b... more In this paper, we establish some common fixed point theorems for selfmappings in uniform spaces by employing the concepts of an A-distance and an E-distance introduced by Aamri and El Moutawakil [3] as well as the notion of comparison functions. We employ a more general contractive definition than that of Aamri and El Moutawakil [3]. Our results are generalizations of Theorems 3.1-3.3 of [3] and those of Olatinwo [12, 13].