ALGORITHMS FOR A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND A COUNTABLE FAMILY OF SOME NONLINEAR MULTI-VALUED NONEXPANSIVE-TYPE MAPS  

作　　者：Ogonnaya Michael ROMANUS Ukamaka Victoria NNYABA Monday Ogudu NNAKWE 

机构地区：[1]Department of Pure and Applied Mathematics, African University of Science and Technology

出　　处：《Acta Mathematica Scientia》2018年第6期1805-1820,共16页数学物理学报（B辑英文版）

摘　　要：In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.

关 键 词：Halpern-type algorithm Krasnoselskii-type algorithm system of generalizedmixed equilibrium problems totally quasi-C-asymptotically nonexpansive multi-valued maps equally continuous maps 

分 类 号：O177.91[理学—数学]