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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: 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: 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: 9Citation - Scopus: 10Last Remarks on g-metric Spaces and Related Fixed Point Theorems(Springer-verlag Italia Srl, 2016) 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.
