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Numerical Algorithms

, Volume 73, Issue 3, pp 869–906 | Cite as

Iterative algorithms for solving variational inequalities and fixed point problems for asymptotically nonexpansive mappings in Banach spaces

  • Gang Cai
  • Yekini Shehu
  • Olaniyi Samuel Iyiola
Original Paper

Abstract

The purpose of this paper is to study some iterative algorithms for finding a common element of the set of solutions of systems of variational inequalities for inverse-strongly accretive mappings and the set of fixed points of an asymptotically nonexpansive mapping in uniformly convex and 2-uniformly smooth Banach space or uniformly convex and q-uniformly smooth Banach space. Strong convergence theorems are obtained under suitable conditions. We also give some numerical examples to support our main results. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.

Keywords

Variational inequality Fixed point Strong convergence Asymptotically nonexpansive mapping Banach space 

Mathematics Subject Classification (2010)

49J30 47H10 47H17 49M05 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Gang Cai
    • 1
  • Yekini Shehu
    • 2
  • Olaniyi Samuel Iyiola
    • 3
  1. 1.School of Mathematics ScienceChongqing Normal UniversityChongqingChina
  2. 2.Department of MathematicsUniversity of NigeriaNsukkaNigeria
  3. 3.Department of Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeUSA

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