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Existence and convergence of fixed points for noncyclic $\varphi$-contractions | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 5، شماره 3، 2024، صفحه 267-274 اصل مقاله (390.3 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.21992.1127 | ||
| نویسنده | ||
| Akram Safari-Hafshejani* | ||
| Department of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 19395-3697, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Fixed point؛ Best proximity point؛ Noncyclic $\varphi$-contractions؛ Uniformly convex Banach spaces | ||
| مراجع | ||
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