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SINGLE PROJECTION ALGORITHM FOR VARIATIONAL INEQUALITIES IN BANACH SPACES WITH APPLICATION TO CONTACT PROBLEM

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Acta Mathematica Scientia 2020年第4期40卷 1045-1063页

作者： yekini shehu Department of Mathematics Zhejiang Norrmal UniversityJinhua 321004China

We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach *** underline cost function of the variational inequality is assumed to be monotone and Lipschitz continuous.A weak convergence result is obtained under reasonable assumptions on the variable *** also give the strong convergence result for when the underline cost function is strongly monotone and Lipchitz *** this strong convergence case,the proposed method does not require prior knowledge of the modulus of strong monotonicity and the Lipschitz constant of the cost function as input parameters,rather,the variable step-sizes are diminishing and *** asymptotic estimate of the convergence rate for the strong convergence case is also *** completeness,we give another strong convergence result using the idea of Halpern iteration when the cost function is monotone and Lipschitz continuous and the variable step-sizes are bounded by the inverse of the Lipschitz constant of the cost ***,we give an example of a contact problem where our proposed method can be applied.

关键词： variational inequality 2-uniformly convex Banach space Tseng’s algorithm strong convergence rate of convergence

CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

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Acta Mathematica Scientia 2014年第4期34卷 1081-1097页

作者： yekini shehu Department of Mathematics University of NigeriaNsukkaNigeria

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.

关键词： left Bregman strongly relatively nonexpansive mapping left Bregman projection equilibrium problem Banach spaces

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

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Acta Mathematica Scientia 2014年第2期34卷 409-423页

作者： yekini shehu Department of Mathematics University of Nigeria

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.

关键词： Pseudo-contractive mappings reflexive Banach spaces uniformly Gateaux differentiable norm variational inequality

CONVERGENCE OF HYBRID VISCOSITY AND STEEPEST-DESCENT METHODS FOR PSEUDOCONTRACTIVE MAPPINGS AND NONLINEAR HAMMERSTEIN EQUATIONS

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Acta Mathematica Scientia 2018年第2期38卷 610-626页

作者： yekini shehu Olaniyi.S.IYIOLA Department of Mathematics University of Nigeria Department of Mathematics Minnesota State University

In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （assuming existence） and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.

关键词： Lipschitz pseudocontractive mapping monotone operators equations of Hammerstein type strong convergence Hilbert spaces

Further Investigation into Split Common Fixed Point Problem for Demicontractive Operators

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Acta Mathematica Sinica,English Series 2016年第11期32卷 1357-1376页

作者： yekini shehu Oluwatosin T.MEWOMO Department of Mathematics University of Nigeria School of Mathematics Statistics and Computer ScienceUniversity of Kwazulu Natal

Our contribution in this paper is to propose an iterative algorithm which does not reqmre prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these Mgorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the Mgorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.

关键词： Demicontractive mappings split common fixed point problems iterative scheme strongconvergence Hilbert spaces

q-一致光滑、一致凸Banach空间中关于变分不等式问题和严格伪压缩映射的不动点问题的粘性迭代算法

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数学物理学报（A辑） 2016年第4期36卷 623-638页

作者：蔡钢 yekini shehu 重庆师范大学数学科学学院重庆401331 Department of Mathematics University of Nigeria

该文在q-一致光滑,一致凸Banach空间中研究了关于广义压缩映射的粘性迭代算法,找到了关于两个逆强增生算子的变分不等式问题解集与无限个严格伪压缩映射的公共不动点集的公共元.所得结果提高和推广了许多最近的相关结果.

关键词：不动点变分不等式强收敛伪压缩映射 Banach空间