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AIMS Mathematics

2023, Volume 8, Issue 12: 28582-28600. doi: 10.3934/math.20231463
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Approximating fixed points of demicontractive mappings in metric spaces by geodesic averaged perturbation techniques

  • 1.
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802, Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
  • 2.
    Sule Lamido University Kafin Hausa, Department of Mathematics, Faculty of Natural and Applied Sciences, P.M.B 048, Jigawa, Nigeria
  • 3.
    Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430122 Baia Mare, Romania
  • 4.
    Academy of Romanian Scientists, Ilfov Str. No. 3, 050045 Bucharest, Romania
  • Received: 23 August 2023 Revised: 21 September 2023 Accepted: 09 October 2023 Published: 20 October 2023

  • MSC : 47H05, 47H10, 47H25

  • In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and $ \Delta $-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasi-nonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in Table 1. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces.

    Citation: Sani Salisu, Vasile Berinde, Songpon Sriwongsa, Poom Kumam. Approximating fixed points of demicontractive mappings in metric spaces by geodesic averaged perturbation techniques[J]. AIMS Mathematics, 2023, 8(12): 28582-28600. doi: 10.3934/math.20231463

    Related Papers:

  • In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and $ \Delta $-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasi-nonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in Table 1. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces.


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