On common and sequential fixed points via asymptotic regularity
Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 163-176
https://doi.org/10.4134/CKMS.c210001
Published online December 6, 2021
Printed January 31, 2022
Ravindra Kishor Bisht, Sayantan Panja, Kushal Roy, Mantu Saha
National Defence Academy; The University of Burdwan; The University of Burdwan; The University of Burdwan
Abstract : In this paper, we introduce some new classes of generalized mappings and prove some common fixed point theorems for a pair of asymptotically regular mappings. Our results extend and improve various well-known results due to Kannan, Reich, Wong, Hardy and Rogers, \'Ciri\'c, Jungck, G\'ornicki and many others. In addition to it, a sequential fixed point for a mapping which is the point-wise limit of a sequence of functions satisfying \'Ciri\'c-Proinov-G\'ornicki type mapping has been proved. Supporting examples have been given in strengthening hypotheses of our established theorems.
Keywords : Fixed point, common fixed point, asymptotic regularity, orbital continuity, $k$-continuity, \'Ciri\'c-Proinov-G\'ornicki type mapping
MSC numbers : Primary 47H10; Secondary 54H25
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