A remark on convergence theory for iterative processes of Proinov contraction
Commun. Korean Math. Soc. 2019 Vol. 34, No. 4, 1157-1162
https://doi.org/10.4134/CKMS.c180382
Published online October 31, 2019
Ravindra K. Bisht
National Defence Academy
Abstract : In this paper, we extend the study of general convergence theorems for the Picard iteration of Proinov contraction from the class of continuous mappings to the class of discontinuous mappings. As a by product we provide a new affirmative answer to the open problem posed in \cite{R2}.
Keywords : fixed point, $\varphi$-contraction, Proinov contraction, $k$-continuity
MSC numbers : Primary 47H09, 54E50; Secondary 47H10, 54E40
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