RATIONAL-TYPE CONTRACTIONS IN DOUBLE CONTROLLED METRIC TYPE SPACES WITH APPLICATIONS TO NONLINEAR INTEGRAL EQUATIONS
By
Rajeshvari Dhote1, Manoj Ughade2 and S. S. Shrivastava3
Department of Mathematics, Institute for Excellence in Higher Education (IEHE), Bhopal, Madhya Pradesh, India–462016
Email: rajeshvaridhote13@gmail.com, manojhelpyou@gmail.com, sss.math@yahoo.com
(Received: February 05, 2026, In format: February 26, 2026; Revised: May 17, 2026; Accepted: June 10, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56113
Abstract
In this paper, we introduce several classes of rational-type contractive mappings in double controlled metric type spaces, namely rational, quadratic rational, maximum rational, interpolative rational, and mixed rational contractions. Sufficient conditions are established for the existence of fixed points and the convergence of Picard iterative sequences. Existence and uniqueness results are obtained for the rational, quadratic rational, maximum rational, and mixed rational contractions, while existence together with Picard convergence is proved for the interpolative rational contraction. Several examples are presented to illustrate the applicability of the proposed results. Furthermore, an application to a nonlinear Fredholm integral equation is included to demonstrate the effectiveness of the developed theory.
2020 Mathematical Sciences Classification: Primary 47H10; Secondary 54H25, 54E50, 54E35, 45G10.
Keywords and Phrases: Double controlled metric type space; rational-type contraction; fixed point theorem; Picard iteration; generalized metric space; nonlinear Fredholm integral equation.