Abstract
We introduce and study new types of mixed monotone multivalued mappings in partially ordered complete metric spaces. We give relationships between those two types of mappings and prove their coupled fixed point and coupled common fixed point theorems in partially ordered complete metric spaces. Some examples of each type of mappings satisfying the conditions of the main theorems are also given. Our main result includes several recent developments in fixed point theory of mixed monotone multivalued mappings.
Highlights
Introduction and PreliminariesLet (X, d) be a metric space, and let CB(X) be the class of all nonempty bounded and closed subsets of X
Let (X, ⩽) be a partially ordered set, and suppose that there is a metric d on X such that (X, d) is a complete metric space
In [14], Yin and Guo introduced the new notion of g-monotone mapping and proved some fixed point theorems for multivalued and single valued g-increasing mappings in partially ordered metric spaces
Summary
We introduce and study new types of mixed monotone multivalued mappings in partially ordered complete metric spaces. We give relationships between those two types of mappings and prove their coupled fixed point and coupled common fixed point theorems in partially ordered complete metric spaces. Some examples of each type of mappings satisfying the conditions of the main theorems are given. Our main result includes several recent developments in fixed point theory of mixed monotone multivalued mappings
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