Fractal and Fractional (Dec 2022)

New Results for Weakly Compatible (<i>WC</i>) and <i>R</i>-Weakly Commuting (<i>RWC</i>) Mappings with an Applicationin Dynamic Programming

  • Penumarthy Parvateesam Murthy,
  • Sanjay Kumar,
  • Rajesh Kumar,
  • Pusplata Sahu,
  • Zoran D. Mitrović,
  • Reny George

DOI
https://doi.org/10.3390/fractalfract6120733
Journal volume & issue
Vol. 6, no. 12
p. 733

Abstract

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The aim of this paper is to obtain some new results about common fixed points. Our results use weaker conditions than those previously used. We have relaxed the conditions for commutating pair mappings and compatible mappings of the type (A), which were introduced in 1976. The theorems are enriched by using the concept of WC and various types of weakly commuting pairs of maps in metric spaces. To discuss the existence and uniqueness of the common solutions, we have obtained an application to the functional equations in dynamic programming.

Keywords