Commun. Korean Math. Soc. 2019; 34(4): 1157-1162
Online first article August 27, 2019 Printed October 31, 2019
https://doi.org/10.4134/CKMS.c180382
Copyright © The Korean Mathematical Society.
Ravindra K. Bisht
National Defence Academy
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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