Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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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.

A remark on convergence theory for iterative processes of Proinov contraction

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