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Received December 8, 2016; Accepted March 10, 2017; Published April 2, 2017
Abstract. The purpose of this paper is to define a notion of strictly convex and normal structures in fuzzy metric spaces. Also, a theorem that provides existence of a common fixed point theorem for two self-mappings defined on strictly convex fuzzy metric spaces is proved. In the proof of the main results, topological methods for characterization spaces with nondeterministic distance is used. Moreover, we present the concept of proximal nonexpansive mappings on star-shaped sets in complete fuzzy metric spaces. We also derive some results on the best proximity for these mappings in complete fuzzy metric spaces. Finally, we provide some examples to illustrate our main results.
How to Cite this Article:
M. H. M. Rashid, A common fixed point theorem in strictly convex FM-spaces, Communications in Optimization Theory, Vol. 2017 (2017), Article ID 19, pp. 1-29.