数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1805-1820.

• 论文 • 上一篇    下一篇

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

Ogonnaya Michael ROMANUS, Ukamaka Victoria NNYABA, Monday Ogudu NNAKWE   

  1. Department of Pure and Applied Mathematics, African University of Science and Technology, Abuja, Nigeria
  • 收稿日期:2017-07-17 修回日期:2018-01-15 出版日期:2018-12-25 发布日期:2018-12-28
  • 作者简介:Ogonnaya Michael ROMANUS,E-mail:rromanus@aust.edu.ng;Ukamaka Victoria NNYABA,E-mail:nukamaka@aust.edu.ng;Monday Ogudu NNAKWE,E-mail:mondaynnakwe@gmail.com

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

Ogonnaya Michael ROMANUS, Ukamaka Victoria NNYABA, Monday Ogudu NNAKWE   

  1. Department of Pure and Applied Mathematics, African University of Science and Technology, Abuja, Nigeria
  • Received:2017-07-17 Revised:2018-01-15 Online:2018-12-25 Published:2018-12-28

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 and a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive multi-valued maps are constructed. Strong convergence of the sequence generated by these algorithms 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 class of nonlinear problems.

关键词: Halpern-type algorithm, Krasnoselskii-type algorithm, system of generalized mixed equilibrium problems, totally quasi-φ-asymptotically nonexpansive multi-valued maps, equally continuous maps

Abstract: 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 and a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive multi-valued maps are constructed. Strong convergence of the sequence generated by these algorithms 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 class of nonlinear problems.

Key words: Halpern-type algorithm, Krasnoselskii-type algorithm, system of generalized mixed equilibrium problems, totally quasi-φ-asymptotically nonexpansive multi-valued maps, equally continuous maps