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Article Citation - WoS: 2Citation - Scopus: 3Lyapunov-Type Inequalities for Lidstone Boundary Value Problems on Time Scales(Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Oguz, Arzu Denk; Ozbekler, AbdullahIn this paper, we establish new Hartman and Lyapunov-type inequalities for even-order dynamic equations x.2n (t) + (-1)n-1q(t) xs (t) = 0 on time scales T satisfying the Lidstone boundary conditions x.2i (t1) = x.2i (t2) = 0; t1, t2. [t0,8) T for i = 0, 1,..., n - 1. The inequalities obtained generalize and complement the existing results in the literature.Article Citation - WoS: 8Citation - Scopus: 8Berinde Mappings in Ordered Metric Spaces(Springer-verlag Italia Srl, 2015) Karapinar, Erdal; Sadarangani, KishinRecently, Samet and Vetro proved a fixed point theorem for mappings satisfying a general contractive condition of integral type in orbitally complete metric spaces (Samet and Vetro, Chaos Solitons Fractals 44:1075-1079, 2011). Our aim in this paper is to present a version of the results obtained in the above mentioned paper in the context of ordered metric spaces. Some examples are presented to distinguish our results from the existing ones.Article Citation - WoS: 13Citation - Scopus: 16A Remark on "existence and Uniqueness for a Neutral Differential Problem With Unbounded Delay Via Fixed Point Results F-Metric Spaces"(Springer-verlag Italia Srl, 2019) Aydi, Hassen; Karapinar, Erdal; Mitrovic, Zoran D.; Rashid, TawseefVery recently, Hussain and Kanwal (Trans A Razmadze Math Inst 172(3): 481-490, 2018) proved some (coupled) fixed point results in this setting for a -.-contractive mappings on the setting of F-metric spaces that was initiated by Jleli and Samet (Fixed Point Theory Appl 2018: 128, 2018). In this note, we underline that the proof of Hussain and Kanwal (Trans A Razmadze Math Inst 172(3): 481-490, 2018) has a gap. We provide two examples to illustrate our observation. We also correct the proof and improved the result by replacing a-admissibility by orbital a-admissibility.Editorial Pontine Capillary Telangiectasia Mimicking Active Demyelinating Plaque in a Patient With Multiple Sclerosis(Springer-verlag Italia Srl, 2023) Koksal, Ali; Kiziloglu, Alper; Ogul, Hayri[No Abstract Available]Article Citation - WoS: 51Citation - Scopus: 58F-Contraction Mappings on Metric-Like Spaces in Connection With Integral Equations on Time Scales(Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.In 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 - WoS: 2Citation - Scopus: 4A Sturm Comparison Criterion for Impulsive Hyperbolic Equations(Springer-verlag Italia Srl, 2020) Ozbekler, Abdullah; Isler, Kubra UsluIn this paper, we investigate the Sturmian comparison theory for hyperbolic equations with fixed moments of effects. The results obtained extend the results of those existing in the literature for Sturmian comparison theory on ordinary and impulsive differential equations to impulsive hyperbolic equations.Article Citation - WoS: 13Citation - Scopus: 13Best Proximity Point Results in Dislocated Metric Spaces Via r-functions(Springer-verlag Italia Srl, 2018) Gholizadeh, Leila; Karapinar, ErdalIn this paper, we investigate the existence of best proximity of R-contractions in the frame of dislocated metric spaces. We also propose some conditions to guarantee the uniqueness of best proximity point for such contractions. We consider an illustrative example to support the given results. This result generalizes a number of recent results on the topic in the literature.Article Citation - WoS: 3Citation - Scopus: 3Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales(Springer-verlag Italia Srl, 2017) Agarwal, Ravi P.; Cetin, Erbil; Ozbekler, AbdullahIn this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.Article Citation - WoS: 141Citation - Scopus: 144Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions(Springer-verlag Italia Srl, 2021) Sevinik-Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.Article Citation - WoS: 40Citation - Scopus: 36Common Fixed Points for Generalized -Implicit Contractions in Partial Metric Spaces: Consequences and Application(Springer-verlag Italia Srl, 2015) Aydi, Hassen; Jellali, Manel; Karapinar, ErdalIn this paper, we introduce the concept of generalized -admissible pair of mappings generalizing the definition of -admissible mappings presented by Samet et al. (Nonlinear Anal 75:2154-2165, 2012). Based on above, we define generalized -implicit contractions in the setting of partial metric spaces and we provide some common fixed point results for such contractions. We also derive some consequences and corollaries from our obtained results. An application and some examples are presented making effective the new concepts and results.
