Ulam-Hyers Stability and Well-posedness of the Fixed Point Problems for Contractive Multi-valued Operator in \(b\)-metric Spaces

Supak Phiangsungnoen


In this paper, we establish some fixed point results for new classes of contractive multivalued mappings via \(\alpha_*\)-admissible mapping with respect to \(\eta\) in the class of \(b\)-metric spaces. To illustrate the obtained results, we provide some example. We also study the generalized Ulam-Hyers stability and well-posedness of fixed point problems are given. The theorems presented will extend, generalize or unify several statements currently exist in the literature on those topics.


\(\alpha\)-admissible mappings; \(b\)-metric spaces; Fixed points; Multi-valued operator; Ulam-Hyers stability; Well-posedness

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