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

Atanas Ilchev, Rumen Marinov, Diana Nedelcheva and Boyan Zlatanov ()
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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

Mathematics, 2025, vol. 13, issue 20, 1-14

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.

Keywords: coupled fixed point; set-valued mapping; quasi-metric space; q 0 -symmetry; approximate fixed point; nonlinear analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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