Papers by Godwin A . Okeke
This work approximates the solution of two-level variational inequality and fixed point problem i... more This work approximates the solution of two-level variational inequality and fixed point problem in a real Hilbert space where the underlying operators are pseudo-monotone and ϱ-demimetric. An iterative algorithm was developed and shown to converge strongly to the solution set of two-level variational inequality and fixed point problem. Four numerical examples are presented to further demonstrate the usefulness and applicability of our method. The result obtained extends, generalizes and compliments several existing results in this direction of research.
In this paper, we study the convergence and almost sure (S, T)−stability of Jungck-Noor type, Jun... more In this paper, we study the convergence and almost sure (S, T)−stability of Jungck-Noor type, Jungck-SP type, Jungck-Ishikawa type and Jungck-Mann type random iterative algorithms for some kind of a general contractive type random operators (2.14) in a separable Banach spaces. The Bochner integrability of random fixed point of this kind of random operators, the convergence and almost sure (S, T)−stability for these kind of random iterative algorithms under condition (18) are obtained. Our results are stochastic generalizations of Zhang et al. [1], Okeke and Eke [2] and many others in deterministic verse.
Applied Mathematical Sciences, 2015
In this paper, we prove some fixed point results for some classes of nonlinear mappings recently ... more In this paper, we prove some fixed point results for some classes of nonlinear mappings recently introduced by Okeke and Olaleru [5]. Our results improves several other known results in literature, including the results of Sahu et al. [8] and Sahu [7].
British Journal of Mathematics & Computer Science, 2013
Arab Journal of Mathematical Sciences
PurposeThis paper aims to prove some fixed-point theorems for a general class of mappings in modu... more PurposeThis paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.Research limitations/implicationsAnalytical and theoretical results.Practical implicationsThe results of this paper can be applied in science and engineering.Social implicationsThe results of this paper is applicable in certain soci...
Arab Journal of Mathematical Sciences
PurposeThe authors prove the existence and uniqueness of fixed point of mappings satisfying Gerag... more PurposeThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.Research limitations/implicationsThe results are theoretical and analytical.Practical implicationsThe results were applied to solving nonlinear integral equations.Social implicationsThe results ...
The Journal of Analysis, 2022
The Journal of Analysis, 2022
Mathematical Methods in the Applied Sciences, 2022
We propose a three-step iteration process for finding the common fixed points of nonexpansive map... more We propose a three-step iteration process for finding the common fixed points of nonexpansive mapping and strongly pseudocontractive mapping in a real Banach space. We weaken the necessity of condition (C) imposed by a previous study on the mappings by using a quite simple and different method to obtain strong convergence of our proposed iterative scheme to the common fixed point of nonexpansive mapping and strongly pseudocontractive mapping. Numerically, we also show that our proposed iterative scheme converges faster than some existing iterative schemes. Furthermore, we apply our proposed iterative process in solving mixed type Volterra-Fredholm functional nonlinear integral equations and delay differential equations.
Axioms, 2020
We propose two new iterative algorithms for solving K-pseudomonotone variational inequality probl... more We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish some strong convergence theorems for our newly developed methods under certain restriction. Our results extend and improve several recently announced results. Furthermore, we give several numerical experiments to show that our proposed algorithms performs better in comparison with several existing methods.
Applied General Topology, 2020
It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some... more It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.
Discrete Dynamics in Nature and Society, 2020
In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a f... more In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a faster iterative process and propose a faster fixed-point iterative method for finding the solution of two-point boundary value problems. We prove analytically and with series of numerical experiments that the Picard–Ishikawa hybrid iterative process has the same rate of convergence as the CR iterative process.
Arab Journal of Mathematical Sciences, 2018
We approximate the fixed points of contraction mappings using the Picard-Krasnoselskii hybrid ite... more We approximate the fixed points of contraction mappings using the Picard-Krasnoselskii hybrid iterative process, which is known to converge faster than all of Picard, Mann and Ishikawa iterations in complex valued Banach spaces. Moreover, we prove analytically and with a numerical example that the Picard-Mann hybrid iteration and the Picard-Krasnoselskii hybrid iteration have the same rate of convergence. Furthermore, we apply our results in finding solutions of delay differential equations in complex valued Banach spaces.
Arabian Journal of Mathematics, 2017
The purpose of this paper is to introduce Picard-Krasnoselskii hybrid iterative process which is ... more The purpose of this paper is to introduce Picard-Krasnoselskii hybrid iterative process which is a hybrid of Picard and Krasnoselskii iterative processes. In case of contractive nonlinear operators, our iterative scheme converges faster than all of Picard, Mann, Krasnoselskii and Ishikawa iterative processes in the sense of Berinde (Iterative approximation of fixed points, 2002). We support our analytic proofs with a numerical example. Using this iterative process, we also find the solution of delay differential equation.
Journal of Inequalities and Applications, 2015
The aim of this paper is to introduce the concept of generalized φ-weakly contraction random oper... more The aim of this paper is to introduce the concept of generalized φ-weakly contraction random operators and then to prove the convergence and almost sure T-stability of Mann and Ishikawa-type random iterative schemes. We also prove that a random fixed point of such operators is Bochner integrable. Our results generalize, extend and improve various results in the existing literature including the results in Berinde (Bul.
Abstract and Applied Analysis, 2012
A new concept of the asymptotically weakG-pseudo-Ψ-contractive non-self-mappingT:G↦Bis introduced... more A new concept of the asymptotically weakG-pseudo-Ψ-contractive non-self-mappingT:G↦Bis introduced and some strong convergence theorems for the mapping are proved by using the generalized projection method combined with the modified successive approximation method or with the modified Mann iterative sequence method in a uniformly and smooth Banach space. The proof methods are also different from some past common methods.
We prove the existence of a unique ?xed point for a mapping satisfying a rational type contractiv... more We prove the existence of a unique ?xed point for a mapping satisfying a rational type contractive inequality condition in complex-valued Banach spaces. We approximate this fixed point via some ?xed point iterative processes with high rate of convergence.
Communications in Mathematics and Applications, 2018
Existence of a unique and bounded stochastic solution of integral nonclassical ordinary different... more Existence of a unique and bounded stochastic solution of integral nonclassical ordinary differential equation is studied using the method of integral contractor operators.
Nonlinear functional analysis and applications, 2018
Recently, Olaleru and Okeke [19] introduced the class of asymptotically demicon- tractive mapping... more Recently, Olaleru and Okeke [19] introduced the class of asymptotically demicon- tractive mappings in the intermediate sense as a generalization of the class of asymptotically demicontractive mappings. The authors proved some convergence theorems for this class of nonlinear mappings in Hilbert spaces (see, [19]). The purpose of this paper is to continue the study of this class of nonlinear mappings. We prove some fixed point theorems for the class of asymptotically demicontractive mappings in the intermediate sense. We also prove some mean convergence theorems for this class of mappings in Hilbert spaces.
Uploads
Papers by Godwin A . Okeke