Fixed point theorems on generalized metric spaces for mappings in a class of almost \(\varphi\)-contractions
In this paper, the authors obtained some sufficient conditions for the existence and uniqueness of fixed point for a contraction mapping satisfying an implicit relation in the framework of generalized metric space in the sense of \textit{A. Branciari} [Publ. Math. 57, No. 1--2, 31--37 (2000; Zbl 0963.54031)]. The results obtained generalize and extend the corresponding results of \textit{V. Berinde} [Nonlinear Anal. Forum 9, No. 1, 43--53 (2004; Zbl 1078.47042)], \textit{R. M. Tiberio Bianchini} [Boll. Unione Mat. Ital., IV. Ser. 5, 103--108 (1972; Zbl 0249.54023)], \textit{R. Kannan} [Am. Math. Mon. 76, 405--408 (1969; Zbl 0179.28203)] and of \textit{S. Reich} [Can. Math. Bull. 14, 121--124 (1971; Zbl 0211.26002)].
scientific article; zbMATH DE number 6476933
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