Ulam-Hyers stability results for fixed point problems via \(\alpha\)-\(\psi\)-contractive mapping in \((b)\)-metric space. (English) Zbl 1434.54013
Summary: We will investigate some existence, uniqueness, and Ulam-Hyers stability results for fixed point problems via \(\alpha\)-\(\psi\)-contractive mapping of type-\((b)\) in the framework of \(b\)-metric spaces. The presented theorems extend, generalize, and unify several results in the literature, involving the results of B. Samet et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2154–2165 (2012; Zbl 1242.54027)].
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
| 39B82 | Stability, separation, extension, and related topics for functional equations |
Keywords:
Hyers-Ulam stability; fixed point problems; \(\alpha\)-\(\psi\)-contractive mapping; \((b)\)-metric spaceCitations:
Zbl 1242.54027References:
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