Abstract
Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ciric obtained a coupled coincidence and coupled common fixed point of two single valued maps. In this article, we extend these concepts to multi-valued mappings and obtain coupled coincidence points and common coupled fixed point theorems involving hybrid pair of single valued and multi-valued maps satisfying generalized contractive conditions in the frame work of a complete metric space. Two examples are presented to support our results. 2000 Mathematics Subject Classification: 47H10; 47H04; 47H07.
Highlights
Introduction and preliminariesLet (X, d) be a metric space
We denote the set of coupled coincidence point of mappings F and g by C(F, g)
Ćirić et al [4] proved coupled common fixed point theorems for mappings satisfying nonlinear contractive conditions in partially ordered complete metric spaces and generalized the results given in [3]
Summary
Introduction and preliminariesLet (X, d) be a metric space. For x Î X and A ⊆ X, we denote d(x, A) = inf{d(x, A): y Î A}. We denote the set of coupled coincidence point of mappings F and g by C(F, g). Ćirić et al [4] proved coupled common fixed point theorems for mappings satisfying nonlinear contractive conditions in partially ordered complete metric spaces and generalized the results given in [3].
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