SOME INVARIANT POINT RESULTS FOR RATIONAL CONTRACTIONS INVOLVING CONTROL FUNCTIONS IN R-METRIC SPACE

Abstract

The main purpose of the research is to establish some invariant point resultsunder the purview of R-Metric Spaces. For that purpose, the concept of control functionsunder the framework of R-metric space is used for rational type contraction. To the bestof known literatures, this kind of work in the said space has not yet been found. Moreover,the concepts of R-preserving, R-continuous, R-contraction, R-convergence and R-Cauchysequence have also been used for the said space. In addition to it, some corollaries have beenrepresented as special cases of the established results. Also, some examples and applicationshave been developed to illustrate the established results and underscore its importance.