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Coupled Fixed Points in ( q 1 , q 2 )-Quasi-Metric Spaces

Author

Listed:
  • Atanas Ilchev

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Rumen Marinov

    (Department of Mathematics and Physics, Faculty of Electrical Engineering, Technical University of Varna, 1 Studentska Str., 9000 Varna, Bulgaria)

  • Diana Nedelcheva

    (Department of Mathematics and Physics, Faculty of Electrical Engineering, Technical University of Varna, 1 Studentska Str., 9000 Varna, Bulgaria)

  • Boyan Zlatanov

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

Abstract

This paper presents a new coupled fixed-point theorem for a pair of set-valued mappings acting on the Cartesian product of ( m 1 , m 2 ) - and ( n 1 , n 2 ) -quasi-metric spaces. Within the general, non-symmetric quasi-metric setting, we establish the existence of an approximate coupled fixed point. Moreover, under the additional assumption of q 0 -symmetry, we guarantee the existence of a coupled fixed point. Together, these results extend and unify several known theorems in fixed-point theory for quasi-metric and asymmetric spaces. We illustrate the obtained results regarding fixed points when the underlying space is equipped with a graph structure and, thus, sufficient conditions are found to guarantee the existence of a subgraph with a loop with a length greater than or equal to 2.

Suggested Citation

  • Atanas Ilchev & Rumen Marinov & Diana Nedelcheva & Boyan Zlatanov, 2025. "Coupled Fixed Points in ( q 1 , q 2 )-Quasi-Metric Spaces," Mathematics, MDPI, vol. 13(20), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:20:p:3242-:d:1768024
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