Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON COMMON AND SEQUENTIAL FIXED POINTS VIA ASYMPTOTIC REGULARITY

  • Received : 2021.01.02
  • Accepted : 2021.08.23
  • Published : 2022.01.31
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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.

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Acknowledgement

The authors are thankful to the referee for his/her valuable suggestions for the improvement of the paper. Sayantan Panja and Kushal Roy both acknowledge the support of the Council of Scientific and Industrial Research (CSIR), New Delhi, India. Due to the policy of the journal which requires to list authors surnames in alphabetical order, the order of authors is looking like this. However, the order of the authors should be read as K. Roy, S. Panja, M. Saha and R. K. Bisht.

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