Implicit Midpoint Scheme for Enriched Nonexpansive Mappings

Authors

  • Sani Salisu Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University Kafin Hausa, Jigawa, Nigeria https://orcid.org/0000-0003-3387-4188
  • Lukman Hashim Umaru Ali Shinkafi Polytechnic Sokoto. Sokoto, Nigeria
  • Adamu Yusuf Inuwa Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano. Kano, Nigeria.
  • Abbas Umar Saje Sule Lamido University Kafin Hausa, Jigawa, Nigeria

Keywords:

Enriched nonexpansive mapping, Implicit midpoint scheme, Fixed point, Hilbert space, Stiff equation

Abstract

In this article, an implicit scheme for approximating fixed points of enriched nonexpansive mappings is proposed and analyzed. The scheme is structured based on the implicit midpoint rule of certain ordinary differential equation due to stiffness. Convergence properties of the scheme are analyzed, and the scheme is shown to iteratively approach a fixed point of the underlined mapping. Numerical illustrations are given to show the implementation of the scheme with respect to certain enriched mappings.

Author Biographies

Sani Salisu, Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University Kafin Hausa, Jigawa, Nigeria

B.Sc. M.Sc. and PhD. in Mathematics

Lukman Hashim, Umaru Ali Shinkafi Polytechnic Sokoto. Sokoto, Nigeria

Department of Mathematics, Faculty of Science, Umaru Ali Shinkafi Polytechnic Sokoto. Sokoto, Nigeria

Adamu Yusuf Inuwa, Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano. Kano, Nigeria.

B.Sc. M.Sc. and PhD. in Mathematics

Abbas Umar Saje, Sule Lamido University Kafin Hausa, Jigawa, Nigeria

Department of Science Education, Faculty of Education, Sule Lamido University Kafin Hausa, Jigawa, Nigeria

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Published

2022-12-21

How to Cite

Salisu, S., Hashim, L., Inuwa, A. Y., & Saje, A. U. (2022). Implicit Midpoint Scheme for Enriched Nonexpansive Mappings. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 1(2), 211–225. Retrieved from https://bangmodjmcs.com/index.php/ncao/article/view/88

Issue

Vol. 1 No. 2 (2022): July - December, 2022

Section

Articles

License

Copyright (c) 2022 ani Salisu, Lukman Hashim, Adamu Yusuf Inuwa, Abbas Umar Saje

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