Some critical remarks on recent results concerning \(\digamma\)-contractions in \(b\)-metric spaces. (English) Zbl 1518.54034
Summary: This paper aims to correct recent results on a generalized class of \(\digamma\)-contractions in the context of \(b\)-metric spaces. The significant work consists of repairing some novel results involving \(\digamma\)-contraction within the structure of \(b\)-metric spaces. Our objective is to take advantage of the property (F1) instead of the four properties viz. (F1), (F2), (F3) and (F4) applied in the results of M. Nazam et al. [Nonlinear Anal., Model. Control 23, No. 5, 664–690 (2018; Zbl 1420.54083)]. Our approach of proving the results utilizing only the condition (F1) enriches, improves, and condenses the proofs of a multitude of results in the existing state-of-art.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H10 | Fixed-point theorems |
| 54E40 | Special maps on metric spaces |
Keywords:
\(\digamma\)-contraction; \(b\)-common fixed point; \(b\)-metric space; \(\upsilon_s\)-completeCitations:
Zbl 1420.54083References:
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