20 results
Search Results
Now showing 1 - 10 of 20
Article Citation - WoS: 5Citation - Scopus: 4Some remarks on 'Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces'(Springer international Publishing Ag, 2014) Agarwal, Ravi P.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoThe main aim of this paper is to advise researchers in the field of Fixed Point Theory against an extended mistake that can be found in some proofs. We illustrate our claim proving that theorems in the very recent paper (Wang in Fixed Point Theory Appl. 2014: 137, 2014) are incorrect, and we provide different corrected versions of them.Article Citation - WoS: 5Citation - Scopus: 11Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces(Hindawi Ltd, 2014) Agarwal, Ravi P.; Alsulami, Hamed H.; Karapinar, Erdal; Khojasteh, FarshidVery recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.Article Citation - WoS: 35Citation - Scopus: 43Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives(Springer, 2018) Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Ozbekler, AbdullahWe state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.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: 19Citation - Scopus: 21Lyapunov Type Inequalities for Mixed Nonlinear Riemann-Liouville Fractional Differential Equations With a Forcing Term(Elsevier, 2017) Agarwal, Ravi P.; Ozbekler, AbdullahIn this paper, we present some new Lyapunov and Hartman type inequalities for Riemann-Liouville fractional differential equations of the form ((a)D(alpha)x)(t) + p(t) vertical bar x(t) vertical bar(mu-1) x(t) + q(t) vertical bar x(t) vertical bar(gamma-1) x(t) = f(t), where p, q, f are real-valued functions and 0 < gamma < 1 < mu < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier B.V. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 10Lyapunov Type Inequalities for Nth Order Forced Differential Equations With Mixed Nonlinearities(Amer inst Mathematical Sciences-aims, 2016) Agarwal, Ravi P.; Ozbekler, AbdullahIn the case of oscillatory potentials, we present Lyapunov type inequalities for nth order forced differential equations of the form x((n))(t) + Sigma(m)(j=1) qj (t)vertical bar x(t)vertical bar(alpha j-1)x(t)= f(t) satisfying the boundary conditions x(a(i)) = x(1)(a(i)) = x(11)(ai) = center dot center dot center dot = x((ki))(ai) = 0; i = 1, 2,..., r, where a(1) < a(2) < ... < a(r), 0 <= k(i) and Sigma(r)(j=1) k(j) + r = n: r >= 2. No sign restriction is imposed on the forcing term and the nonlinearities satisfy 0 < alpha(l) < ... < alpha a(j) < 1 < alpha a(j+1) < ... < alpha(m) < 2. The obtained inequalities generalize and compliment the existing results 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: 57Citation - Scopus: 74Further Fixed Point Results on g-metric Spaces(Springer int Publ Ag, 2013) Karapinar, Erdal; Agarwal, Ravi P.Very recently, Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) noticed that some fixed point theorems in the context of a G-metric space can be deduced by some well-known results in the literature in the setting of a usual (quasi) metric space. In this paper, we note that the approach of Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) is inapplicable unless the contraction condition in the statement of the theorem can be reduced into two variables. For this purpose, we modify some existing results to suggest new fixed point theorems that fit with the nature of a G-metric space. The expressions in our result, the contraction condition, cannot be expressed in two variables, therefore the techniques used in (Int. J. Anal. 2013: 917158, 2013; Fixed Point Theory Appl. 2012: 210, 2012) are not applicable.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.
