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Article Citation - WoS: 17Citation - Scopus: 27Fixed Point Theorems in New Generalized Metric Spaces(Springer Basel Ag, 2016) Karapinar, Erdal; Karapınar, Erdal; O'Regan, Donal; Roldan Lopez de Hierro, Antonio Francisco; Shahzad, Naseer; Karapınar, Erdal; Mathematics; MathematicsThe aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.Article Citation - WoS: 16Citation - Scopus: 19Fixed Point Theorems in Quasi-Metric Spaces and Applications To Multidimensional Fixed Point Theorems on g-metric Spaces(Yokohama Publ, 2015) Agarwal, Ravi; Karapinar, Erdal; Roldan-Lopez-De-Hierro, Antonio-Francisco; MathematicsIn this manuscript, we investigate the equivalence of the coupled fixed point theorems in quasi-metric spaces and in G-metric spaces. We also notice that coupled fixed point theorems in the setting of G-metric spaces can be derived from their corresponding versions in quasi-metric spaces. Our results generalize and unify several fixed point theorems in the context of G-metric spaces in the literature.Article Citation - WoS: 2Citation - Scopus: 2A Schwarz Problem for the Generalized Beltrami Equation(Taylor & Francis Ltd, 2011) Yuksel, UgurThis article deals with the Schwarz problem [image omitted] where is a regular domain of the complex plane. Sufficient conditions on the coefficients of the differential equation are obtained under which the operator of the corresponding problem for a system of integral equations is contractive in a certain Holder space. This leads to the existence of a unique solution of the original problem.
