Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

Abstract

In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.

Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

“…More precisely, they fit better for modeling the practical real world situations by the less requirements they have in their statements. Some applications are in works like [32,34]. Applications and real-world illustrations on similar lines can be explored for our present result and also for similar other results in future works.…”

Common Fixed Point Theorem for Multivalued Mappings Using Ternary Relation in G -Metric Space with an Application

“…Motivated by Alam and Imdad [14] and Perveen et al [21], we introduce the following definitions and proposition for multivalued mapping in the context of G-metric space setting. Definition 21.…”

“…For more results on binary relation, one can see [15][16][17][18][19][20] and the references therein. Perveen et al [21] gave the prove in relation theoretic common fixed point results for generalized weak nonlinear contractions with an application. Hossain et al [22] gave the study of relation-theoretic metrical fixed point theorem for rational type contraction mapping with an application.…”