Abstract
Abstract In this paper, we provide coincidence point and fixed point theorems satisfying an implicit relation, which extends and generalizes the result of Gregori and Sapena, for set-valued mappings in complete partially ordered fuzzy metric spaces. Also we prove a fixed point theorem for set-valued mappings on complete partially ordered fuzzy metric spaces which generalizes results of Mihet and Tirado. MSC:54E40, 54E35, 54H25.
Highlights
In this paper, we provide coincidence point and fixed point theorems satisfying an implicit relation, which extends and generalizes the result of Gregori and Sapena, for set-valued mappings in complete partially ordered fuzzy metric spaces
Some fixed point results for set-valued mappings on fuzzy metric space can be found in [, ] and references therein
The aim of this paper is to prove a coincidence point and fixed point theorem on a partially ordered fuzzy metric space satisfying an implicit relation and another fixed point theorem
Summary
Since F is a set-valued fuzzy order ψ -contraction of ( , λ)-type mapping, there exists x ∈ Fx with x x such that M(x , x , t) > – ψ(δ) Repeating this argument, we get a sequence {xn} in Y such that xn+ ∈ Fxn with xn xn+ and such that. Are, respectively, generalizations of the theorems of Mihet [ ] and Tirado [ ] to the set-valued case in partial ordered fuzzy metric spaces. We introduce a definition and, by using it, we shall state fixed and common fixed point theorems in the partially ordered fuzzy metric space. Of [ ] to set-valued mappings in complete partially ordered fuzzy metric spaces. Because F is a fuzzy order K -set-valued mapping, there exists x ∈ Fx such that x x and
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