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Article Citation - WoS: 17Citation - Scopus: 20Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces(Hindawi Ltd, 2015) De la Sen, Manuel; Karapinar, ErdalThis paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of p-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the p-composite mappings restricted to each of the p subsets in the cyclic disposal are also investigated and some illustrative examples are given.Article Citation - WoS: 38Citation - Scopus: 48Fixed Points of Modified f-contractive Mappings in Complete Metric-Like Spaces(Hindawi Ltd, 2015) Alsulami, Hamed H.; Karapinar, Erdal; Piri, HosseinWe introduce the notion of modified F-contractive mappings in the setting of complete metric-like spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature.Article Citation - WoS: 4Citation - Scopus: 6On the Oscillation of Even-Order Nonlinear Differential Equations With Mixed Neutral Terms(Hindawi Ltd, 2021) Kaabar, Mohammed K. A.; Özbekler, Abdullah; Grace, Said R.; Alzabut, Jehad; Ozbekler, Abdullah; Siri, Zailan; Özbekler, Abdullah; Mathematics; MathematicsThe oscillation of even-order nonlinear differential equations (NLDiffEqs) with mixed nonlinear neutral terms (MNLNTs) is investigated in this work. New oscillation criteria are obtained which improve, extend, and simplify the existing ones in other previous works. Some examples are also given to illustrate the validity and potentiality of our results.Article Citation - WoS: 104Citation - Scopus: 113(α,ψ)-meir-keeler Contraction Mappings in Generalized b-metric Spaces(Hindawi Ltd, 2018) Karapinar, Erdal; Czerwik, Stefan; Aydi, HassenWe present a fixed point theorem for generalized (alpha, Psi)-Meir-Keeler type contractions in the setting of generalized b-metric spaces. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.Article Citation - WoS: 9Citation - Scopus: 10(α-Ψ) Mappings on Generalized Quasimetric Spaces(Hindawi Ltd, 2014) Karapinar, Erdal; Lakzian, HoseinWe consider the existence of a fixed point of (alpha - psi)-contractive mappings in the context of generalized quasimetric spaces without Hausdorff assumption. The obtained results extend several results on the topic in the literature.Article Citation - WoS: 6Citation - Scopus: 6Some Extensions of Fixed Point Results Over Quasi-js-spaces(Hindawi Ltd, 2016) Noorwali, Maha; Alsulami, Hamed H.; Karapinar, ErdalWe introduce the notion of quasi-JS-metric space. After defining the basic topological properties of quasi-JS-metric space, we investigate fixed point of certain mapping in the frame of complete quasi-JS-metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi-b-metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature.Article Citation - WoS: 15Citation - Scopus: 16Ulam-Hyers Stability for Mkc Mappings Via Fixed Point Theory(Hindawi Ltd, 2016) Hassan, Anisa Mukhtar; Karapinar, Erdal; Alsulami, Hamed H.We consider some extension of MKC mappings in the framework of complete dislocated metric spaces. Besides the theoretical results, we also consider some illustrative examples. Further, we state and prove that our main results improved the related results in the frame of generalized Ulam-Hyers stability theory.Article Citation - WoS: 44Citation - Scopus: 49On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory(Hindawi Ltd, 2017) Alharbi, Areej S. S.; Alsulami, Hamed H.; Karapinar, ErdalWe investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of complete b-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.Article Citation - WoS: 1Citation - Scopus: 2Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term(Hindawi Ltd, 2020) Selvam, A. George Maria; Alzabut, Jehad; Jacintha, Mary; Ozbekler, AbdullahThe paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Delta[psi(lambda)z(eta) (lambda)] + p(lambda)z(eta) (lambda) + q(lambda)F(Sigma(lambda-1+mu)(s=lambda 0) (lambda - s - 1)((-mu)) y(s)) = , where z(lambda) = a(lambda) + b(lambda)Delta(mu) y(lambda), Delta(mu) stands for the fractional difference operator in Riemann-Liouville settings and of order mu, 0 < mu <= 1, and eta >= 1 is a quotient of odd positive integers and lambda is an element of N lambda 0+1-mu. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.
