Relation theoretic contractions and their applications in b-metric like spaces

We introduce a relational generalized Meir-Keeler contraction and a relational generalized Meir-Keeler contraction with rational terms in non-complete relational b-metric like spaces in order to establish non-unique fixed point results for a discontinuous single-valued map. Also, we provide an illustrative example to demonstrate that a relational generalized Meir-Keeler contraction with rational terms in a relational b-metric like space admits discontinuity at the fixed point. Thereby,we provide a novel explanation via a binary relation to the question of the existence of a contractive map admitting a fixed point at the point of discontinuity. Finally, we give applications to solve an initial value problem and a non-linear matrix equation which demonstrate the usability and effectiveness of our results.

---

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).