Existence and convergence of fixed point results for noncyclic $\varphi$-contractions

Document Type : Original Article


Department of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 19395-3697, Tehran, Iran


In the paper, we introduce a new class of noncyclic $\varphi$-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Espínola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic $\varphi$-contractions as a consequence of our main theorems.


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