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On the Best Proximity Points for p –Cyclic Summing Contractions

Author

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  • Miroslav Hristov

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, 115 Universitetska str., 9700 Shumen, Bulgaria)

  • Atanas Ilchev

    (Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Assen str., 4000 Plovdiv, Bulgaria)

  • Boyan Zlatanov

    (Department of Real Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Assen str., 4000 Plovdiv, Bulgaria)

Abstract

We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p –cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1060-:d:378965
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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.
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