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Error estimates for approximation of coupled best proximity points for cyclic contractive maps

Author

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  • Ilchev, A.
  • Zlatanov, B.

Abstract

We enrich the known results about coupled fixed and best proximity points of cyclic contraction ordered pair of maps. The uniqueness of the coupled best proximity points for cyclic contraction ordered pair of maps in a uniformly convex Banach space is proven. We find a priori and a posteriori error estimates for the coupled best proximity points, obtained by sequences of successive iterations, when the underlying Banach space has modulus of convexity of power type. A looser conditions are presented for the existence and uniqueness of coupled fixed points of a cyclic contraction ordered pair of maps in a complete metric space and a priori, a posteriori error estimates and the rate of convergence for the coupled fixed points are obtained for the sequences of successive iterations. We apply these results for solving systems of integral equations, systems of linear and nonlinear equations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:412-425
    DOI: 10.1016/j.amc.2016.06.022
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    Cited by:

    1. Miroslav Hristov & Atanas Ilchev & Boyan Zlatanov, 2020. "On the Best Proximity Points for p –Cyclic Summing Contractions," Mathematics, MDPI, vol. 8(7), pages 1-11, July.
    2. 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.
    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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