Browsing by Author "Gulyaz, Selma"
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Article Citation Count: 9A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation(Springer international Publishing Ag, 2013) Yüce, İlker Savaş; Karapinar, Erdal; Karapınar, Erdal; MathematicsIn this manuscript, we discuss the existence of a coupled coincidence point for mappings and , where F has the mixed g-monotone property, in the context of partially ordered metric spaces with an implicit relation. Our main theorem improves and extends various results in the literature. We also state some examples to illustrate our work. MSC: 47H10, 54H25, 46J10, 46J15.Article Citation Count: 21A COUPLED FIXED POINT RESULT IN PARTIALLY ORDERED PARTIAL METRIC SPACES THROUGH IMPLICIT FUNCTION(Hacettepe Univ, Fac Sci, 2013) Karapınar, Erdal; Karapinar, Erdal; MathematicsIn this manuscript, we discuss the existence of coupled fixed points in the context of partially ordered metric spaces through implicit relations for mappings F:X x X -> X such that F has the mixed monotone property. Our main theorem improves and extends various results in the literature. We also state an example to illustrate our work.Article Citation Count: 4Existence of a solution of integral equations via fixed point theorem(Springeropen, 2013) Karapınar, Erdal; Karapinar, Erdal; Rakocevic, Vladimir; Salimi, Peyman; MathematicsIn this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.Article Citation Count: 2Existence of solutions of integral equations via fixed point theorems(Springeropen, 2014) Erhan, İnci; Erhan, Inci M.; MathematicsExistence and uniqueness of fixed points of a mapping defined on partially ordered G-metric spaces is discussed. The mapping satisfies contractive conditions based on certain classes of functions. The results are applied to the problems involving contractive conditions of integral type and to a particular type of initial value problems for the nonhomogeneous heat equation in one dimension. This work is a generalization of the results published recently in (Gordji et al. in Fixed Point Theory Appl. 2012:74, 2012, doi:10.1186/1687-1812-2012-74) to G-metric space.Article Citation Count: 27Fixed Point Theorems for a Class of α-Admissible Contractions and Applications to Boundary Value Problem(Hindawi Publishing Corporation, 2014) Erhan, İnci; Gulyaz, Selma; Karapınar, Erdal; Erhan, Inci M.; MathematicsA class of alpha-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.Article Citation Count: 2Fixed points of α-admissible Meir-Keeler contraction mappings on quasi-metric spaces(Springer international Publishing Ag, 2015) Erhan, İnci; Gulyaz, Selma; Erhan, Inci M.; MathematicsWe introduce alpha-admissible Meir-Keller and generalized alpha-admissible Meir-Keller contractions on quasi-metric spaces and discuss the existence of fixed points of such contractions. We apply our results to G-metric spaces and express some fixed point theorems in G-metric spaces as consequences of the results in quasi-metric spaces.Article Citation Count: 16Generalized α -Meir-Keeler Contraction Mappings on Branciari b-metric Spaces(Univ Nis, Fac Sci Math, 2017) Erhan, İnci; Karapinar, Erdal; Karapınar, Erdal; MathematicsIn this paper, alpha-Meir-Keeler and generalized alpha-Meir-Keeler contractions on Branciari b-metric spaces are introduced. Existence and uniqueness of fixed points of such contractions are discussed and related theorems are proved. Various consequences of the main results are also presented.Article Citation Count: 61An Ulam stability result on quasi-b-metric-like spaces(Sciendo, 2016) Erhan, İnci; Gulyaz, Selma; Karapınar, Erdal; Erhan, Inci M.; MathematicsIn this paper a class of general type alpha-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.