Abstract
In this paper we define convex, strict convex and normal structures for sets in fuzzy cone metric spaces. Also, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition will be proved, using the notion of strictly convex structure. Moreover, we give some examples illustrate our results.
Highlights
The Banach Contraction Mapping Principle [2] is one of the most important theorems in functional analysis
One of the most important of them is the introduction of a nonlinear contractive principle by Boyd and Wong [3]
Huang and Zhang [11] introduced the notion of cone metric spaces by replacing real numbers with an ordered Banach space and proved some fixed point theorems for contractive mappings between these spaces
Summary
The Banach Contraction Mapping Principle [2] is one of the most important theorems in functional analysis. The notion of fuzzy cone metric spaces, as a generalization of the corresponding notions of fuzzy metric spaces by George and Veeramani was introduced by Oner, Kandemir and Tanay [14] They studied topology, convergence of sequences, continuity of mappings, defined the completeness of these spaces, etc. In this paper, using the notion of strictly convex structure for fuzzy cone metric space the existence and uniqueness of a fixed point for non-self mappings with non- linear contractive condition for function φ : P → P , will be proved. In the proof of the main result topological methods for characterization spaces with nondeterministic distances will be used
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