Browsing by Author "Erhan, Inci M."
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Article Citation Count: 0APPLICATIONS OF NON-UNIQUE FIXED POINT THEOREM OF CIRIC TO NONLINEAR INTEGRAL EQUATIONS(int Center Scientific Research & Studies, 2019) Sevinik-Adiguzel, Rezan; Karapinar, Erdal; Erhan, Inci M.In this paper we discuss the application of the non-unique fixed point theorem of Ciric to nonlinear Fredholm integral equations. We establish an existence theorem for the solutions of such integral equations and apply the theorem to particular examples.Article Citation Count: 53Best Proximity Point on Different Type Contractions(Natural Sciences Publishing Corp-nsp, 2011) Karapinar, Erdal; Erhan, Inci M.In this manuscript, some proximity points are obtained by using different types cyclic contractions. Also, generalized cyclic Meir Keeler contraction is introduced and a new fixed point theorem for this cyclic mapping is stated.Article Citation Count: 19Best proximity points of generalized almost ψ-Geraghty contractive non-self-mappings(Springer international Publishing Ag, 2014) Erhan, İnci; Karapinar, Erdal; Karapınar, Erdal; Salimi, Peyman; MathematicsIn this paper, we introduce the new notion of almost psi-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature.Article Citation Count: 1Common fixed point of multifunctions on partial metric spaces(Springer international Publishing Ag, 2015) Erhan, İnci; Erhan, Inci M.; Kutbi, Marwan A.; Shokouhnia, Masoumeh; MathematicsIn this paper, some multifunctions on partial metric space are defined and common fixed points of such multifunctions are discussed. The results presented in the paper generalize some of the existing results in the literature. Several conclusions of the main results are given.Article Citation Count: 9Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations(Springer international Publishing Ag, 2015) Erhan, İnci; Zada, Mian Bahadur; Erhan, Inci M.; MathematicsIn this article, using the common (CLR) property, common fixed point results for two pairs of weakly compatible mappings satisfying contractive condition of integral type on metric spaces are established. Furthermore, the existence and uniqueness of common solution for system of functional equations arising in dynamic programming are discussed as an application of a common fixed point theorem presented in this paper.Article Citation Count: 11Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions(Hindawi Ltd, 2012) Erhan, İnci; Karapinar, Erdal; Karapınar, Erdal; MathematicsWe prove coupled coincidence point and coupled fixed point results of F : X x X -> X and g : X -> X involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.Article Citation Count: 13Coupled fixed point theorems on partially ordered G-metric spaces(Springer int Publ Ag, 2012) Erhan, İnci; Kumam, Poom; Karapınar, Erdal; MathematicsThe purpose of this paper is to extend some recent coupled fixed point theorems in the context of partially ordered G-metric spaces in a virtually different and more natural way.Article Citation Count: 44Cyclic contractions and fixed point theorems(Univ Nis, Fac Sci Math, 2012) Erhan, İnci; Erhan, Inci M.; Karapınar, Erdal; MathematicsIn this manuscript, the existence and uniqueness of fixed points of a class of cyclic operators defined on a closed subset of a Banach space is discussed. Fixed point theorems for some contractions from this class are introduced and illustrative examples are given.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: 37F-contraction mappings on metric-like spaces in connection with integral equations on time scales(Springer-verlag Italia Srl, 2020) Aksoy, Ümit; Aksoy, Umit; Erhan, İnci; Karapınar, Erdal; MathematicsIn this paper we investigate the existence and uniqueness of fixed points of certain (phi,F)-type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular example which demonstrates our theoretical results.Article Citation Count: 3A fixed point theorem for Meir-Keeler type contraction via Gupta-Saxena expression(Springer international Publishing Ag, 2015) Erhan, İnci; Dehici, Abdelkader; Erhan, Inci M.; MathematicsIn this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6: 162-169, 2013), we establish a new fixed point theorem for a Meir-Keeler type contraction via Gupta-Saxena rational expression which enables us to extend and generalize their main result (Gupta and Saxena in Math. Stud. 52: 156-158, 1984). As an application we derive some fixed points of mappings of integral type.Article Citation Count: 11Fixed point theorems for (α, ψ)-Meir-Keeler-Khan mappings(int Scientific Research Publications, 2015) Redjel, Najeh; Dehici, Abdelkader; Karapinar, Erdal; Erhan, Inci M.In this paper, we establish fixed point theorems for a (alpha, psi)-Meir-Keeler-Khan self mappings. The main result of our work is an extension of the theorem of Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste. Vol VIII, Fase., 10 (1976), 1-4]. We also give some consequences. (C)2015 All rights reserved.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: 0FIXED POINT THEOREMS FOR MAPPINGS WITH A CONTRACTIVE ITERATE AT A POINT IN MODULAR METRIC SPACES(House Book Science-casa Cartii Stiinta, 2022) Aksoy, Ümit; Aksoy, Umit; Erhan, İnci; Karapınar, Erdal; MathematicsIn this manuscript, we introduce two new types of contraction, namely, w-contraction and strong Sehgal w-contraction, in the framework of modular metric spaces. We indicate that under certain assumptions, such mappings possess a unique fixed point. For the sake of completeness, we consider examples and an application to matrix equations.Article Citation Count: 164Fixed point theorems for operators on partial metric spaces(Pergamon-elsevier Science Ltd, 2011) Erhan, İnci; Erhan, Inci M.; Karapınar, Erdal; MathematicsFixed point theorems for operators of a certain type on partial metric spaces are given. Orbitally continuous operators on partial metric spaces and orbitally complete partial metric spaces are defined, and fixed point theorems for these operators are given. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation Count: 23Fixed Point Theorems in Complete Modular Metric Spaces and an Application to Anti-periodic Boundary Value Problems(Univ Nis, Fac Sci Math, 2017) Aksoy, Ümit; Karapinar, Erdal; Erhan, İnci; Karapınar, Erdal; MathematicsIn this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Caratheodory's type is considered in the framework of modular metric spaces.Article Citation Count: 36Fixed points of (ψ, φ) contractions on rectangular metric spaces(Springer international Publishing Ag, 2012) Erhan, İnci; Karapinar, Erdal; Karapınar, Erdal; MathematicsExistence and uniqueness of fixed points of a general class of (psi, phi) contractive mappings on complete rectangular metric spaces are discussed. One of the theorems is a generalization of a fixed point theorem recently introduced by Lakzian and Samet. Fixed points of (psi, phi) contractions under conditions involving rational expressions are also investigated. Several particular cases and applications as well as an illustrative example are given.Article Citation Count: 67FIXED POINTS OF GENERALIZED α-ADMISSIBLE CONTRACTIONS ON b-METRIC SPACES WITH AN APPLICATION TO BOUNDARY VALUE PROBLEMS(Yokohama Publ, 2016) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.A general class of alpha-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations.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.