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

Document Type : Original Article

Author

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

Abstract

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. Esp´ınola, 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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References

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AUT Journal of Mathematics and Computing
Volume 5, Issue 3
2024
Pages 267-274

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