On ψg–interpolative Hardy–Rogers type contractions over rqpb space with an application in solving non-linear Fredholm integral equation

Abstract

In the present study, the concept of a new type of contraction namelyψ1–interpolative Hardy–Rogers contraction is introduced which is a unification of g-interpolation and Hardy-Rogers contraction. By utilizing this concept, unique results of the existence of fixed points in the extent of rectangular quasi–partial–metric space are proved. The validity of the obtained results is verified with the help of comparative examples with vivid representations. The existence of a solution to the Fredholm integral equation is also
provided here via a fixed point for such mappings,