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Best proximity points of (EP)-operators with qualitative analysis and simulation

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  • Usurelu, Gabriela Ioana
  • Turcanu, Teodor

Abstract

In this paper, we analyze a Thakur three-step iterative process adapted for the context of non-self-mappings. Based on this iteration, we state and prove the existence of best proximity points for the recently introduced class of (EP)-non-self-mappings. Under certain assumptions, we study the convergence of the considered Thakur process to a best proximity point for the same class of operators. Moreover, we design a CQ-type algorithm which strongly converges to a best proximity point of such kind of mappings. In addition, we present the CQ-variant of the proposed algorithm that strongly converges to a best proximity pair. Some examples and numerical simulations sustain the efficiency of our new algorithms.

Suggested Citation

  • Usurelu, Gabriela Ioana & Turcanu, Teodor, 2021. "Best proximity points of (EP)-operators with qualitative analysis and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 215-230.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:215-230
    DOI: 10.1016/j.matcom.2021.02.022
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    References listed on IDEAS

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    1. Ilchev, A. & Zlatanov, B., 2016. "Error estimates for approximation of coupled best proximity points for cyclic contractive maps," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 412-425.
    2. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    3. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.
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