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Common fixed point of nonlinear contractive mappings

  • Received: 18 August 2022 Revised: 22 September 2022 Accepted: 25 September 2022 Published: 09 October 2022
  • MSC : 47H10, 54H25

  • The purpose of this paper is to study the existence of a common fixed point for a pair of mappings without assumption of the contractive coefficient being fixed and less than 1. By replacing the fixed contractive coefficient with a nonlinear contractive function, we establish a unique common fixed point theorem for a pair of asymptotically regular self-mappings with either orbital continuity or $ q $-continuity in a metric space. Moreover, by the asymptotical regularity of two approximate mappings, we prove that a pair of nonexpansive and continuous self-mappings, which are defined on a nonempty closed convex subset of a Banach space, have a common fixed point. Some examples are given to illustrate that our results are extensions of a recent result in the existing literature.

    Citation: Hui Huang, Xue Qian. Common fixed point of nonlinear contractive mappings[J]. AIMS Mathematics, 2023, 8(1): 607-621. doi: 10.3934/math.2023028

    Related Papers:

  • The purpose of this paper is to study the existence of a common fixed point for a pair of mappings without assumption of the contractive coefficient being fixed and less than 1. By replacing the fixed contractive coefficient with a nonlinear contractive function, we establish a unique common fixed point theorem for a pair of asymptotically regular self-mappings with either orbital continuity or $ q $-continuity in a metric space. Moreover, by the asymptotical regularity of two approximate mappings, we prove that a pair of nonexpansive and continuous self-mappings, which are defined on a nonempty closed convex subset of a Banach space, have a common fixed point. Some examples are given to illustrate that our results are extensions of a recent result in the existing literature.



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