Coupled Coincidence and Common Fixed Point Theorems for Mappings in Partially Ordered Metric Spaces

Abstract

Abstract:In this paper, we prove coupled coincidence points and common fixed points theorem for two mappings satisfying various contractive conditions in partially ordered metric spaces. Our results will generalize and extend some recent results in fixed point theory.

COMMON FIXED POINT RESULTS FOR INFINITE FAMILIES IN PARTIALLY ORDERED b-METRIC SPACES AND APPLICATIONS Vol. 4(2) July. 2016, No. 6, pp. 56-67 K. ZARE, R. ARAB

“…(a) φ(t) < ψ(t) for each t > 0, φ(0) = ψ(0) = 0; (b) φ and ψ are continuous functions; (c) ψ is increasing. We denote by Θ the set of all functions θ : [0, ∞) 4 −→ [0, ∞) satisfying the following conditions:…”

“…During the last few decades, there have appeared a lot of papers on common fixed points of metric spaces, b-metric spaces, G-metric spaces and partial metric spaces with different methods(see for example [2,4,5,6,7,15,16,20]. The family of contraction mappings was introduced and studied by Ćirić [10] and Tasković [21].…”

Coincidence of Fixed Points with Mixed Monotone Property

“…Definition 5 13 : Let ℳ be a nonempty set ℱ and 𝑇are commutative if for all 𝓂, 𝓃 ∈ ℳ, ℱ(𝑇𝓃, 𝑇𝓂) = 𝑇(ℱ(𝓃, 𝓂)). Definition 6 14 :The function 𝜓: [0, ∞) → [0, ∞) is called an altering distance function if satisfying the following conditions: i-𝜓 is a continuous ii-ii -𝜓nondecreasing function iii-𝜓(𝑡) = 0 ↔ 𝑡 = 0, and 𝜙: [0, ∞) → [0, ∞) satisfying the following conditions: i-𝜙 is lower semi-continuous, ii-𝜙(𝑡) = 0 ↔ 𝑡 = 0.…”