%0 Journal Article
%T Existence and convergence of fixed points for noncyclic $\varphi$-contractions
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Safari-Hafshejani, Akram
%D 2024
%\ 07/01/2024
%V 5
%N 3
%P 267-274
%! Existence and convergence of fixed points for noncyclic $\varphi$-contractions
%K Fixed point
%K Best proximity point
%K Noncyclic $\varphi$-contractions
%K Uniformly convex Banach spaces
%R 10.22060/ajmc.2023.21992.1127
%X 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.
%U https://ajmc.aut.ac.ir/article_5171_015ab466f7cb2f573695a8f71ef898e6.pdf