Research Article Open Access

Convergence Results for Fixed Point Problems of Accretive Operators in Banach Spaces

Chioma Lydia Ejikeme1, Mujahid Abbas2 and Dennis Ferdinand Agbebaku1
  • 1 University of Nigeria, Nigeria
  • 2 Government College University, Pakistan
Journal of Mathematics and Statistics
Volume 16 No. 1, 2020, 161-169

DOI: https://doi.org/10.3844/jmssp.2020.161.169

Published On: 31 July 2020

How to Cite: Ejikeme, C. L., Abbas, M. & Agbebaku, D. F. (2020). Convergence Results for Fixed Point Problems of Accretive Operators in Banach Spaces. Journal of Mathematics and Statistics, 16(1), 161-169. https://doi.org/10.3844/jmssp.2020.161.169

Abstract

This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three - step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined in a Hilbert space was obtained. Numerical illustration with graphical display of the convergence of the sequence obtained from the iterative scheme is also presented.

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Keywords

  • Banach Spaces
  • Accretive Operators
  • Resolvents
  • Fixed Point