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Article Citation - WoS: 9Citation - Scopus: 10Some Fixed Point Results on Interpolative Metric Spaces(Pergamon-elsevier Science Ltd, 2025) Karapinar, Erdal; Agarwal, Ravi P.This paper aims to introduce some basic fixed point theorems on interpolative metric space that is a natural extension of standard metric space.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: 15Citation - Scopus: 16Disconjugacy Via Lyapunov and Vallee-Poussin Type Inequalities for Forced Differential Equations(Elsevier Science inc, 2015) Agarwal, Ravi P.; Ozbekler, AbdullahIn the case of oscillatory potentials, we present some new Lyapunov and Vallee-Poussin type inequalities for second order forced differential equations. No sign restriction is imposed on the forcing term. The obtained inequalities generalize and compliment the existing results in the literature. (C) 2015 Elsevier Inc. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 6Lyapunov Type Inequalities for Second Order Sub and Super-Half Differential Equations(Dynamic Publishers, inc, 2015) Agarwal, Ravi P.; Ozbekler, Abdullah; MathematicsIn the case of oscillatory potential, we present a Lyapunov type inequality for second order differential equations of the form (r(t)Phi(beta)(x'(t)))' + q(t)Phi(gamma)(x(t)) = 0, in the sub-half-linear (0 < gamma < beta) and the super-half-linear (0 < beta < gamma < 2 beta) cases where Phi(*)(s) = vertical bar s vertical bar*(-1)s.Review Citation - WoS: 3Citation - Scopus: 3Lyapunov Type Inequalities for Second Order Forced Mixed Nonlinear Impulsive Differential Equations(Elsevier Science inc, 2016) Agarwal, Ravi P.; Ozbekler, AbdullahIn this paper, we present some new Lyapunov and Hartman type inequalities for second order forced impulsive differential equations with mixed nonlinearities: x ''(t) + p(t)vertical bar x(t)vertical bar(beta-1)x(t) + q(t)vertical bar x(t)vertical bar(gamma-1)x(t) = f(t), t not equal theta(i); Delta x'(t) + p(i)vertical bar x(t)vertical bar(beta-1)x(t) + q(i)vertical bar x(t)vertical bar(gamma-1) x(t) = f(i), t = theta(i), where p, q, f are real-valued functions, {p(i)}, {q(i)}, {f(i)} are real sequences and 0 < gamma < 1 < beta < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f and the sequences {p(i)}, {q(i)}, {f(i)}. The inequalities obtained generalize and complement the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier Inc. All rights reserved.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: 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.
