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Ćirić-Type Operators and Common Fixed Point Theorems

Author

Listed:
  • Claudia Luminiţa Mihiţ

    (Department of Mathematics and Computer Science, “Aurel Vlaicu” University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania
    These authors contributed equally to this work.)

  • Ghiocel Moţ

    (Department of Mathematics and Computer Science, “Aurel Vlaicu” University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania
    These authors contributed equally to this work.)

  • Gabriela Petruşel

    (Department of Business, Babeş-Bolyai University Cluj-Napoca, Horea Street no. 7, 400174 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we establish existence, uniqueness and approximation results for the common fixed point. In the same framework, the second problem is to study various stability properties. More precisely, we will obtain sufficient conditions assuring that the common fixed point problem is well-posed and has the Ulam–Hyers stability, as well as the Ostrowski property for the considered problem. Some examples and applications are finally given in order to illustrate the abstract theorems proposed in the first part of the paper. Our results extend and complement some theorems in the recent literature.

Suggested Citation

  • Claudia Luminiţa Mihiţ & Ghiocel Moţ & Gabriela Petruşel, 2022. "Ćirić-Type Operators and Common Fixed Point Theorems," Mathematics, MDPI, vol. 10(11), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1947-:d:832595
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    References listed on IDEAS

    as
    1. A. Petruşel & I. A. Rus, 2019. "Graphic Contraction Principle and Applications," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Mathematical Analysis and Applications, pages 411-432, Springer.
    2. V. Berinde & A. Petruşel & I. A. Rus & M. A. Şerban, 2016. "The Retraction-Displacement Condition in the Theory of Fixed Point Equation with a Convergent Iterative Algorithm," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 75-106, Springer.
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