Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces
Summary: By giving a counter-example, we point out a gap in the paper by the first author [Adv. Theory Nonlinear Anal. Appl. 2, No. 2, 85--87 (2018; Zbl 1412.47137)] where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich-Rus-Ćirić in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by \textit{S. Reich} is not applicable [Can. Math. Bull. 14, 121--124 (1971; Zbl 0211.26002); Boll. Unione Mat. Ital., IV. Ser. 5, 26--42 (1972; Zbl 0249.54026); Boll. Unione Mat. Ital., IV. Ser. 4, 1--11 (1971; Zbl 0219.54042)].
interpolative Reich-Rus-Ćirić type contraction
scientific article; zbMATH DE number 6994859