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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14411/18
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Article Citation - WoS: 2Citation - Scopus: 5A Sturm Comparison Criterion for Impulsive Hyperbolic Equations(Springer-verlag Italia Srl, 2020-02-01) Ozbekler, Abdullah; Isler, Kubra Uslu; Uslu İşler, KübraIn 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: 14Citation - Scopus: 17A Remark on "existence and Uniqueness for a Neutral Differential Problem With Unbounded Delay Via Fixed Point Results F-Metric Spaces"(Springer-verlag Italia Srl, 2019-05-14) 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.Article Citation - WoS: 2Citation - Scopus: 3Lyapunov-Type Inequalities for Lidstone Boundary Value Problems on Time Scales(Springer-verlag Italia Srl, 2020-03-12) Agarwal, Ravi P.; Oguz, Arzu Denk; Ozbekler, Abdullah; Denk Oğuz, ArzuIn 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: 54Citation - Scopus: 64F-Contraction Mappings on Metric-Like Spaces in Connection With Integral Equations on Time Scales(Springer-verlag Italia Srl, 2020-06-07) 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: 13Citation - Scopus: 15Best Proximity Point Results in Dislocated Metric Spaces Via <i>r</I>-functions(Springer-verlag Italia Srl, 2017-09-05) 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: 2Citation - Scopus: 3Isometric Structure of Transportation Cost Spaces on Finite Metric Spaces(Springer-verlag Italia Srl, 2022-07-20) Ostrovska, Sofiya; Ostrovskii, Mikhail, IThe paper is devoted to isometric Banach-space- theoretical structure of transportation cost (TC) spaces on finite metric spaces. The TC spaces arc also known as Arens-Eells, Lipschitzfree, or Wasserstein spaces. A new notion of a roadmap pertinent to a transportation problem on a finite metric space has been introduced and used to simplify proofs for the results on representation of TC spaces as quotients of l(1) spaces on the edge set over the cycle space. A Tolstoi-type theorem for roadmaps is proved, and directed subgraphs of the canonical graphs, which are supports of maximal optimal roadmaps, are characterized. Possible obstacles for a TC space on a finite metric space X preventing them from containing subspaces isometric to l(infinity)(n) have been found in terms of the canonical graph of X. The fact that TC spaces on diamond graphs do not contain l(infinity)(4) isometrically has been derived. In addition, a short overview of known results on the isometric structure of TC spaces on finite metric spaces is presented.Editorial Pontine Capillary Telangiectasia Mimicking Active Demyelinating Plaque in a Patient With Multiple Sclerosis(Springer-verlag Italia Srl, 2022-12-06) Koksal, Ali; Kiziloglu, Alper; Ogul, Hayri[No Abstract Available]Article Citation - WoS: 40Citation - Scopus: 38Common Fixed Points for Generalized -Implicit Contractions in Partial Metric Spaces: Consequences and Application(Springer-verlag Italia Srl, 2014-08-19) 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.Article Citation - WoS: 8Citation - Scopus: 8Berinde Mappings in Ordered Metric Spaces(Springer-verlag Italia Srl, 2014-08-19) 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: 9Citation - Scopus: 10Last Remarks on <i>g</I>-metric Spaces and Related Fixed Point Theorems(Springer-verlag Italia Srl, 2015-08-06) Agarwal, Ravi P.; Karapinar, Erdal; Roldan Lopez de Hierro, Antonio FranciscoIn this report, we present some new fixed points theorems in the context of quasi-metric spaces that can be particularized in a wide range of different frameworks (metric spaces, partially ordered metric spaces, G-metric spaces, etc.). Our contractivity conditions involve different classes of functions and we study the case in which they only depend on a unique variable. Furthermore, we do not only introduce new contractivity conditions, but also expansivity conditions. As a consequence of our results, we announce that many fixed point results in G-metric spaces can be derived from the existing results if all arguments are not distinct.