Abstract
AbstractIn this article, we study the existence of coupled coincidence points for multi-valued nonlinear contractions in partially ordered metric spaces. We do it from two different approaches, the first is Δ-symmetric property recently studied in Samet and Vetro (Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Anal. 74, 4260-4268 (2011)) and second one is mixed g-monotone property studied by Lakshmikantham and Ćirić (Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70, 4341-4349 (2009)).The theorems presented extend certain results due to Ćirić (Multi-valued nonlinear contraction mappings, Nonlinear Anal. 71, 2716-2723 (2009)), Samet and Vetro (Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Anal. 74, 4260-4268 (2011)) and many others. We support the results by establishing an illustrative example.2000 MSC: primary 06F30; 46B20; 47E10.
Highlights
Introduction and preliminariesLet (X, d) be a metric space
Let (X, d) be a complete metric space and let T be a mapping from X into CB(X)
Lakshmikantham and Ćirić [5] proved coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces using mixed g-monotone property
Summary
Introduction and preliminariesLet (X, d) be a metric space. We denote by CB(X) the collection of non-empty closed bounded subsets of X. Suppose that f is lower semi-continuous and that there exists a function j: [0, +∞) ® [a, 1), 0
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