A Relation-Theoretic Matkowski-Type Theorem in Symmetric Spaces

Abstract

In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with a locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. In addition, we adopt an example to substantiate the genuineness of our newly proved result. Finally, as an application of our main result, we establish the existence and uniqueness of a solution of a periodic boundary value problem.

Keywords

• fixed points
• symmetric spaces
• binary relations
• <i>T</i>-transitivity
• regular spaces