A Survey on Approximation of Common Fixed Point of Countably Infinite Family of Nonexpansive Mappings

  • A. G. Okonkwo Department of Mathematics, Nnamdi Azikiwe University, Anambra State, Nigeria.
  • N. N. Araka Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria.
  • K. O. Ibeh Department of Mathematics, Nnamdi Azikiwe University, Anambra State, Nigeria.
  • K. O. Ibeh Department of Mathematics, Nnamdi Azikiwe University, Anambra State, Nigeria.
DOI: https://doi.org/10.6084/m9.figshare.21900864
Keywords: Nonexpansive mappings, Reflexive and strictly convex Banach spaces, Uniformly Gâteaux differentiable norm, Weakly inward.

Abstract

In this paper, strong convergence theorems for approximation of a common fixed point of countably family of nonexpansive mappings in strictly convex reflexive real Banach space with uniformly Gâteaux differentiable norm are proved. Consequently, strong convergence theorems for approximation of a common fixed point of countably infnite family of k-strictly pseudocontractive mappings are proved in strictly convex q-uniformly smooth real Banach spaces. Numerical example is generated to demonstrate workability of an algorithm developed. Our theorems extend, improve and generalize some existing results.

Published
2022-11-22
How to Cite
Okonkwo, A. G., Araka, N. N., Ibeh, K. O., & Ibeh, K. O. (2022). A Survey on Approximation of Common Fixed Point of Countably Infinite Family of Nonexpansive Mappings. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 8(2), 38 - 57. https://doi.org/10.6084/m9.figshare.21900864
Issue
Vol 8 No 2 (2022)
Section
Articles

Copyright (c) 2023 A. G. Okonkwo, N. N. Araka, K. O. Ibeh, K. O. Ibeh

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