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Browsing by Author "Dutta, Hemen"

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    Conference Object
    Inequalities of Bullen's Type for Logarithmically Convexity With Numerical Applications
    (Springer international Publishing Ag, 2020) Kavurmaci-Onalan, Havva; Akdemir, Ahmet Ocak; Dutta, Hemen
    In this study, we consider a familier inequality of Hermite-Hadamard inequality that is well known as Bullen's inequality in the literature. We remind an integral identity that derives Bullen's type integral inequalities. By using this integral identity, we have established new Bullen's type inequalities for functions whose second derivatives in absolute value are logarithmically convex. So, new error bounds for averaged midpoint-trapezoid quadrature rules are obtained and applications in numerical integration are given.
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    Article
    Strongly (Vλ, A, Δ(Vm)n, P)-Summable Sequence Spaces Defined by an Orlicz Function
    (Pergamon-elsevier Science Ltd, 2011) Dutta, Hemen; Bilgin, Tunay
    We introduce the strongly (V-lambda, A, Delta(n)((v,m)) p)-summable sequences and give the relation between the spaces of strongly (V-lambda, A, Delta(n)((v,m)) p)-summable sequences and strongly (V-lambda, A, Delta(n)((v,m)) p)-summable sequences with respect to an Orlicz function when A = (a(ik)) is an infinite matrix of complex numbers, Delta(n)((v,m)) is a generalized difference operator and p = (p(i)) is a sequence of positive real numbers. Also we give natural relationship between strongly (V-lambda, A,Delta(n)((vm)) p)-convergence with respect to an Orlicz function and strongly S-lambda (A,Delta(n)((vm)))-statistical convergence. (C) 2011 Elsevier Ltd. All rights reserved.