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http://dx.doi.org/10.4134/CKMS.c210001

ON COMMON AND SEQUENTIAL FIXED POINTS VIA ASYMPTOTIC REGULARITY  

Bisht, Ravindra Kishor (Department of Mathematics National Defence Academy)
Panja, Sayantan (Department of Mathematics The University of Burdwan)
Roy, Kushal (Department of Mathematics The University of Burdwan)
Saha, Mantu (Department of Mathematics The University of Burdwan)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.1, 2022 , pp. 163-176 More about this Journal
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, Ćirić, Jungck, Górnicki 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 Ćirić-Proinov-Górnicki 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; Ciric-Proinov-Gornicki type mapping;
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