Abstract
In this article, we introduce the notions of cyclic weaker ϕ ○ φ-contractions and cyclic weaker (ϕ, φ)-contractions in complete metric spaces and prove two theorems which assure the existence and uniqueness of a fixed point for these two types of contractions. Our results generalize or improve many recent fixed point theorems in the literature.
Highlights
1 Introduction and preliminaries Throughout this article, by R+, R we denote the sets of all nonnegative real numbers and all real numbers, respectively, while N is the set of all natural numbers
Let (X, d) be a metric space, D be a subset of X and f: D ® X be a map
In 1969, Boyd and Wong [2] introduced the notion of F-contraction
Summary
Introduction and preliminariesThroughout this article, by R+, R we denote the sets of all nonnegative real numbers and all real numbers, respectively, while N is the set of all natural numbers.
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