Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces

The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of left Bregman, strongly asymptotically non-expansive mappings in uniformly convex and uniformly smooth Banach spaces. A strong convergence theorem for the above problems are established. As an application, we solve a generalized mixed equilibrium problem, split Hammerstein integral equations, and a fixed-point problem, and provide a numerical example to support better findings of our result.

[1]  Hong-Kun Xu.  Inequalities in Banach spaces with applications , 1991 .

[2]  O. T. Mewomo,et al.  On split generalised mixed equilibrium problems and fixed-point problems with no prior knowledge of operator norm , 2017 .

[3]  S. Atsushiba.  VISCOSITY APPROXIMATION METHODS FOR FIXED POINTS PROBLEMS , 2011 .

[4]  Fenghui Wang.  A New Algorithm for Solving The Multiple-Sets Split Feasibility Problem in Banach Spaces , 2014 .

[5]  Lu-Chuan Ceng,et al.  Strong convergence of hybrid Bregman projection algorithm for split feasibility and fixed point problems in Banach spaces , 2017 .

[6]  C. E. Chidume,et al.  Approximation of zeros of bounded maximal monotone mappings, solutions of Hammerstein integral equations and convex minimization problems , 2016 .

[7]  Kaleem Raza Kazmi,et al.  An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping , 2014, Optim. Lett..

[8]  Hong-Kun Xu,et al.  Existence and convergence for fixed points of mappings of asymptotically nonexpansive type , 1991 .

[9]  Wataru Takahashi,et al.  Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space , 2007 .

[10]  Abdellatif Moudafi,et al.  Split Monotone Variational Inclusions , 2011, J. Optim. Theory Appl..

[11]  Han,et al.  A general convergence theorem for multiple-set split feasibility problem in Hilbert spaces , 2015 .

[12]  Narin Petrot,et al.  Viscosity Approximation Methods for Split Variational Inclusion and Fixed Point Problems in Hilbert Spaces , 2014 .

[13]  Bin-Chao Deng,et al.  Strong Convergence Theorems for Mixed Equilibrium Problem and Asymptotically I-Nonexpansive Mapping in Banach Spaces , 2014 .

[14]  Hong-Kun Xu,et al.  An Lp inequality and its applications to fixed point theory and approximation theory , 1989 .

[15]  S. Reich,et al.  Right Bregman Nonexpansive Operators in Banach Spaces , 2012 .

[16]  Viorel Barbu,et al.  Nonlinear Differential Equations of Monotone Types in Banach Spaces , 2010 .

[17]  W. Takahashi,et al.  Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups , 2003 .

[18]  Morad Ali Payvand,et al.  System of generalized mixed equilibrium problems, variational inequality, and fixed point problems , 2016 .

[19]  Lishan Liu,et al.  Ishikawa and Mann Iterative Process with Errors for Nonlinear Strongly Accretive Mappings in Banach Spaces , 1995 .

[20]  F. Schöpfer,et al.  An iterative regularization method for the solution of the split feasibility problem in Banach spaces , 2008 .

[21]  S. Reich,et al.  Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces , 2010 .