Abstract
We obtain a new Suzuki type coupled fixed point theorem for a multivalued mappingTfromX×XintoCB(X), satisfying a generalized contraction condition in a complete metric space. Our result unifies and generalizes various known comparable results in the literature. We also give an application to certain functional equations arising in dynamic programming.
Highlights
In 2008, Suzuki [1] introduced a new type of mappings which generalize the well-known Banach contraction principle [2], and, further, Kikkawa and Suzuki [3] proved a Kannan [4] version of mappings
Many fixed point theorems have been proved by various authors as a generalization of Nadler’s theorem [6,7,8,9]
Let (X, d) be a complete metric space and let T be a mapping from X × X into CB(X)
Summary
Introduction and PreliminariesIn 2008, Suzuki [1] introduced a new type of mappings which generalize the well-known Banach contraction principle [2], and, further, Kikkawa and Suzuki [3] proved a Kannan [4] version of mappings.Theorem 1 (see [3]). Let (X, d) be a complete metric space. There exists z ∈ X such that z ∈ Tz. Many fixed point theorems have been proved by various authors as a generalization of Nadler’s theorem [6,7,8,9].
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