A Relation-Theoretic Matkowski-Type Theorem in Symmetric Spaces

• Main Authors: Based Ali, Mohammad Imdad, Salvatore Sessa
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Axioms
• Subjects: fixed points; symmetric spaces; binary relations; <i>T</i>-transitivity; regular spaces
• Online Access: https://www.mdpi.com/2075-1680/10/2/50

In this paper, we present a fixed-point theorem in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>-complete regular symmetric spaces endowed with a locally <i>T</i>-transitive binary relation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula> 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.