Common fixed point theorems under implicit relations on ordered metric spaces and application to integral equations

Abstract

In this paper, we prove existence results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps under implicit relation on ordered orbitally complete metric spaces. We furnish suitable examples to demonstrate the validity of the hypotheses of our results. At the end of the results, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.

Fixed Point Theorems for Mappings Satisfying Implicit Relation in Partial Metric Spaces

“…The introduction of implicit relations in common fixed point theorems was established by V. Popa [16] in . Further many authors extended common fixed point theorems using implicit relations ( [17,18,19,20,21]).…”

Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings Satisfying an Implicit Relation

“…Fixed point theorems satisfying an implicit relation for single-valued and multivalued mappings under different conditions have been studied by various authors including ( [4], [5], [7], [9], [19], [24], [26], [27], [31], [33], [34], [35], [38]). …”

Common coupled fixed point theorems for hybrid pair of mappings satisfying an implicit relation with application

“…Many authors have been studied fixed point theorems satisfying an implicit relation for single-valued and multivalued mappings under different conditions including [4,5,7,20,26,29,[31][32][33]35].…”