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.
Highlights
In 1922, the first prosperous result was postulated by S
We provide an application [18] in a non-linear integral equation to obtain a fixed point
We have established the relation theoretical fixed point results for the rational type contraction
Summary
In 1922, the first prosperous result was postulated by S. Inspired by Turinici’s [9] work, Ran-Reurings in 2004 formulate the result that there will be a fixed point of self-mappings that is applied only for those points which are comparable to each other by an order relation in partial metric space. Alam and Imdad [13] established a profound generalization of the Banach contraction principle with an amorphous binary relation With this structure, various relation-theoretic results were proposed in different aspects of the binary relation or contractive condition. Rodríguez-López [10] and the system of matrix equations by Ran and Reurings [14], the fixed point for iteration to find optimal solution in statistics [15], for the stability problem in Intuitionistics Fuzzy Banach Space [16], and many more such as [17]. We provide an application [18] in a non-linear integral equation to obtain a fixed point
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