Some Fixed Point Results for Two Pairs of Mappings on Integral and Rational Settings

Abstract

 In 2000, P. Hitzler and A.K. Seda (Hitzeler & Seda 2000) obtained a very important generalization of topology which they named as dislocated topology. The corresponding generalized notion of metric obtained from dislocated topology was named as dislocated metric.The fixed point theorem for a single map satisfying contractive condition of integral type with a summable Lebesgue integrable mapping in complete metric space was first time estabished by Branciari (Branciari 2002) in the year 2002. B. E. Rhoades (Rhoades 2003) further extended the theorem of Branciari (Branciari 2002) with a most general contractive condition. Extensions and generalizations for rational and integral type mapping in various spaces can be seen in the literature of fixed point theory. This article establishes some common fixed point results satisfying integral and rational type contractive conditions with common limit range property for two pairs of maps in dislocated metric space. We have established common fixed point result in dislocated metric space with compatible and reciprocal continuity of mappings.