(α, β)-Zb-Geraghty type contraction in b-metric-like spaces via b-simulation function

The aim of this paper is to introduce the notion of (α, β)-Zb-Geraghty type contraction via b-simulation function and use this contraction to establish a common fixed point theorem for a pair of self-mappings in the context of a b-metric-like space. Our result extends and generalizes the result of Matthews [21], Khojasteh et al. [20], Demma et al. [15], Chandok [12] and some others also. We deduce some corollaries from our main result and provide examples to illustrate our results. Moreover, we apply our result to obtain a solution of second order differential equation.Publisher's Versio

A generalization of relation-theoretic contraction principle

In the present paper, we generalize relation-theoretic contraction principle using weaker class of contraction mappings which is assumed to be hold on the elements of a particular subset of the whole space, whose elements are relaxed under the underlying relation. We also relaxed the assumption of continuity from the main result of Alam and Imdad by introducing the notion of (R, k)-continuity. Moreover, our results do not require the underlying binary relation to be T-closed for existence of fixed points in relational metric spaces.Publisher's Versio

Some common fixed point theorems in bipolar metric spaces and applications

In this article, we prove some common fixed point theorems for generalized rational type contractions in bipolar metric spaces. These theorems also generalize and extend several interesting results of metric fixed point theory to the bipolar metric context. In addition, we provide some examples to illustrate our theorems, and applications are obtained in areas of homotopy theory and integral equations by using iterative methods for mathematical operators on a bipolar metric space