Indian Journal of Science and Technology

Abstract

Background/Objectives: In this paper, we introduced the concept of aPf,g integral contractive mappings, which is a new class of integral contractive mappings and using this notion we establish a new fixed point theorem. Findings: Our paper represents a generalization and extension of fixed point theorems for mappings satisfying contractive conditions of integral type where the contractive inequality depends on rational and irrational expression. In particular, we omitted the condition of continuity (which is a very strong condition and appear in almost all papers using contractive mapping of rational type) from many existing results. Application/Improvements: As a direct consequence, some new results of integral type for rational and irrational contraction maps are presented to illustrate our obtained result.

Keywords: Fixed Point, Integral Type, aPf,g–Integral Contractive Mappings, Irrational Type, Rational Type