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
Summary
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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