Abstract
We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.
Highlights
Introduction and PreliminariesLet Ψ be the family of functions ψ : 0, ∞ → 0, ∞ satisfying the following conditions: Ψ1 ψ is nondecreasing; Ψ2 ∞ n1 ψ n t< ∞ for all t > 0, where ψn is the nth iterate of ψ.These functions are known in the literature as c -comparison functions
From our fixed point theorems, we will deduce various fixed point results on metric spaces endowed with a partial order and fixed point results for cyclic contractive mappings
We say that T is a generalized α-ψ contractive mapping if there exist two functions α : X × X → 0, ∞ and ψ ∈ Ψ such that for all x, y ∈ X, and we have α x, y d Tx, Ty ≤ ψ M x, y, 2.1 where M x, y max{d x, y, d x, T x d y, T y /2, d x, T y d y, T x /2}
Summary
Let Ψ be the family of functions ψ : 0, ∞ → 0, ∞ satisfying the following conditions: Ψ1 ψ is nondecreasing; Ψ2. We say that T is an α-ψ contractive mapping if there exist two functions α : X × X → 0, ∞ and ψ ∈ Ψ such that α x, y d T x, T y ≤ ψ d x, y , ∀x, y ∈ X. Let X, d be a complete metric space and T : X → X be an α-ψ contractive mapping. We introduce the concept of generalized α-ψ contractive type mappings, and we study the existence and uniqueness of fixed points for such mappings. From our fixed point theorems, we will deduce various fixed point results on metric spaces endowed with a partial order and fixed point results for cyclic contractive mappings
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
