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Article Citation - WoS: 4Citation - Scopus: 3Existence of solutions of integral equations via fixed point theorems(Springeropen, 2014) Gulyaz, Selma; Erhan, Inci M.Existence 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 - WoS: 40Citation - Scopus: 50Fixed Points of (ψ, Φ) Contractions on Rectangular Metric Spaces(Springer international Publishing Ag, 2012) Erhan, Inci M.; Karapinar, Erdal; Sekulic, TanjaExistence 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 - WoS: 21Citation - Scopus: 23Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, PeymanIn 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 - WoS: 3Citation - Scopus: 6Fixed Points of Α-Admissible Meir-Keeler Contraction Mappings on Quasi-Metric Spaces(Springer international Publishing Ag, 2015) Alsulami, Hamed H.; Gulyaz, Selma; Erhan, Inci M.We 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 - WoS: 18Citation - Scopus: 24Generalized Α -Meir Contraction Mappings on Branciari B-Metric Spaces(Univ Nis, Fac Sci Math, 2017) Gulyaz, Selma; Karapinar, Erdal; Erhan, Inci M.In 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 - WoS: 16Citation - Scopus: 18Weak Ψ-Contractions on Partially Ordered Metric Spaces and Applications To Boundary Value Problems(Springeropen, 2014) Karapinar, Erdal; Erhan, Inci M.; Aksoy, UmitA class of weak psi-contractions satisfying the C-condition is defined on metric spaces. The existence and uniqueness of fixed points of such maps are discussed both on metric spaces and on partially ordered metric spaces. The results are applied to a first order periodic boundary value problem.Article Citation - Scopus: 1Some Remarks About the Existence of Coupled g-coincidence Points(Springeropen, 2015) Erhan, Inci M.; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, NaseerVery recently, in a series of subsequent papers, Nan and Charoensawan introduced the notion of g-coincidence point of two mappings in different settings (metric spaces and G-metric spaces) and proved some theorems in order to guarantee the existence and uniqueness of such kind of points. Although their notion seems to be attractive, in this paper, we show how this concept can be reduced to the unidimensional notion of coincidence point, and how their main theorems can be seen as particular cases of existing results. Moreover, we prove that the proofs of their main statements have some gaps.Article Citation - WoS: 1Citation - Scopus: 2Common Fixed Point of Multifunctions on Partial Metric Spaces(Springer international Publishing Ag, 2015) Aleomraninejad, S. Mohammad Ali; Erhan, Inci M.; Kutbi, Marwan A.; Shokouhnia, MasoumehIn 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 - WoS: 11Citation - Scopus: 8Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.We 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 - WoS: 67An Ulam stability result on quasi-b-metric-like spaces(Sciendo, 2016) Alsulami, Hamed H.; Gulyaz, Selma; Karapinar, Erdal; Erhan, Inci M.In 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.
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