On common and sequential fixed points via asymptotic regularity
Commun. Korean Math. Soc.
Published online December 6, 2021
Ravindra Kishor Bisht, Sayantan Panja, Kushal Roy, and Mantu Saha
NDA Pune; Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India.; Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India.; Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India.
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, $\acute{C}$iri$\acute{c}$, Jungck, G$\acute{o}$rnicki 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 $\acute{C}$iri$\acute{c}$-Proinov-G$\acute{o}$rnicki 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, $\acute{C}$iri$\acute{c}$-Proinov-G$\acute{o}$rnicki type mapping
MSC numbers : Primary 47H10; Secondary 54H25
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