Fixed Point and Coincidence Point Theorems on Banach Spaces over Topological Semifields and Their Applications

H. K. Pathak, R. K. Verma, Brian Fisher

Abstract

We establish some common xed point and coincident point theorems for a quadruple of self-mappings on a Banach space X over a topological semifield.Our first result extends the main result of Pathak et al. [8] to a general class of mappings in which we have dropped the requirement of pairwise commutativity of mappings by imposing certain restrictions on parameters. Our second result deals with the existence of coincidence points for a quadruple of self-mappings under different conditions than in Theorem 1 of [8]. We also discuss an application of our main result to solve certain non-linear function equations in Banach space over a topological semifield.