Abstract

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

Highlights

  • Introduction and preliminariesIn recent years, there appeared a considerable interest in the fixed point theory

  • There appeared a considerable interest in the fixed point theory

  • The main purpose of fixed point theory is to deal with several mappings either of contractive type or non-expansive type in nature over various generalized metric spaces beyond our usual metric spaces and to investigate the existence of their fixed points therein

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Summary

Introduction

Introduction and preliminariesIn recent years, there appeared a considerable interest in the fixed point theory. If (M, d) is a complete metric space and φ : M → [0, ∞) is a lower semi-continuous function, a mapping T : M → M satisfying d(ξ, T ξ) ≤ φ(ξ) − φ(T ξ) for each ξ ∈ M, has a fixed point in M. Ćirić ([4, 5]) had introduced a new contractive condition and proved a prominent fixed point theorem for a quasi contraction mapping.

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