Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

Abstract

Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results.

A Common Fixed Point Theorem for Generalised F -Kannan Mapping in Metric Space with Applications

“…Since then, several researchers involved in investigations of Kannan's contraction mappings using a rectangular property in different spaces. For more details, one can see [12,[17][18][19][20] and the references therein. Furthermore, Morandi and Alimohammadi [16] investigated and extended Kannan's mapping [2] by using the concept due to Branciari [5].…”