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Article Citation - WoS: 40Citation - Scopus: 52Discussion on Generalized-(αψ, Βφ)-Contractive Mappings Via Generalized Altering Distance Function and Related Fixed Point Theorems(Hindawi Ltd, 2014) Berzig, Maher; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoWe extend the notion of (alpha psi, beta phi)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts.Article Citation - WoS: 37Citation - Scopus: 42Fixed Point Results for -Contractive Mappings for a Generalized Altering Distance(Springer international Publishing Ag, 2013) Berzig, Maher; Karapinar, ErdalIn this manuscript, we extend the concept of altering distance, and we introduce a new notion of -contractive mappings. We prove the existence and uniqueness of a fixed point for such mapping in the context of complete metric space. The presented theorems of this paper generalize, extend and improve some remarkable existing results in the literature. We also present several applications and consequences of our results.Letter Citation - WoS: 3Citation - Scopus: 1Comment on "perturbation Analysis of the Nonlinear Matrix Equation x-σi< ai< = q"(Hindawi Ltd, 2013) Berzig, Maher; Karapinar, ErdalWe show that the perturbation estimate for the matrix equation ? ?? - ?? ?? = 1 ?? * ?? ?? ?? ?? ?? ?? = ?? due to J. Li, is wrong. Our discussion is supported by a counterexample.
