A Relation-Theoretic Metrical Fixed Point Theorem for Rational Type Contraction Mapping with an Application

Abstract

In this article, we discuss the relation theoretic aspect of rational type contractive mapping to obtain fixed point results in a complete metric space under arbitrary binary relation. Furthermore, we provide an application to find a solution to a non-linear integral equation.

Common fixed point theorems for interpolative rational-type mapping in complex-valued metric space

“…Electrical engineers benefit from complex numbers when they deal with the fact that the current through a circuit element such as a capacitor or inductor is not in phase with the voltage across it, specifically in the solution of electric equations. This type of work is motivated by [5,14,27,39,46]. The electric circuit can be represented by ternary relation, R a resistor has a unit Ohms (Ω), L an inductor has a unit Henry (H) and C a capacitor has a unit Farad (F ) on V source of power in a series circuit measured in Volt (V ).…”

Almost Boyd-Wong Type Contractions under Binary Relations with Applications to Boundary Value Problems

“…Since than, various results in this direction have been established. To cite some of them, we refer [15][16][17][18][19][20][21][22][23][24][25][26][27] besides others.…”

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

“…Next, to validate the result of Theorem 27, we apply the second-order differential equation (SODE) by transforming it to the system of integral equations. The fixed point theory is involved in physics applications, specifically in the solution of electric equations, and this type of work is motivated from [22,32,33]. It is well known that an electric circuit can be represented by ternary relation, R a resistor, L an inductor, and C a capacitor on E an electromotive force in series.…”

“…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. Further, Gaba et al [23] extended the works of Alam and Imdad [14] by using the Banach contraction mapping principle in generalized metric spaces with a ternary relation.…”