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Some Improvements of Hölder's Inequality on Time Scales

., 326 (2007), no. 1, 228-241. [11] Q. Sheng, M. Fadag, J. Henderson and J. M. Davis, \An exploration of combined dynamic derivatives on time scales and their applications", Nonlinear Anal. Real World Appl., 7 (2006), no. 3, 395-413. [12] Liang-Cheng Wang, “Two Mappings Related to Hölder's Inequality”, Univ. Beograd. Publ. Elektrotehn. Fak., Ser. Mat. 15 (2004), 91-96.

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Jessen's functional, its properties and applications

for convex functions III , J. Math. Anal. Appl. (156) 1 , (1991), 231-239. [20] J.E. Pečarić, I. Rasa, On Jessen’s inequality , Acta. Sci. Math. (Szeged) (56) 3-4 , (1992), 305-309. [21] J.E. Pečarić, F. Proschan, Y.L. Tong, Convex functions, partial orderings, and statistical applications , Academic Press, Inc, 1992. [22] J. Pečarić, V. Šimić, A note on the Hölder inequality , J. Inequal. Pure and Appl. Math. 7 (5) art. 176, (2006), 1-3. [23] I. Rasa, A note on Jessen’s inequality , Itin. Sem

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Existence results for boundary value problems of arbitrary order integrodifferential equations in Banach spaces

Abstract

We study a boundary value problem of fractional integrodifferential equations involving Caputo's derivative of order α ∈ (n-1,n) in a Banach space. Existence and uniqueness results for the problem are established by means of the Hölder's inequality together with some standard fixed point theorems

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Generalized Hermite -Hadamard type integral inequalities for functions whose 3rd derivatives are s-convex

Abstract

In this paper, we have established Hermite-Hadamard type inequalities for functions whose 3rd derivatives are s-convex depending on a parameter. These results have generalized some relationships with [4].

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Some new Ostrowski’s Inequalities for Functions whose nth Derivatives are Logarithmically Convex

Abstract

Some new Ostrowski’s inequalities for functions whose nthderivative are logarithmically convex are established.

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On some new results for non-decreasing sequences

Abstract

In this paper, a general theorem on absolute Riesz summability factors of infinite series is proved under weaker conditions. Also we have obtained some new and known results.

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Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense

Abstract

In this paper we establish some fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense.

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A new application of almost increasing sequences

Abstract

In this paper, a known result dealing with |, pn|k summability of infinite series has been generalized to the φ − |, pn; δ|k summability of infinite series by using an almost increasing sequence.

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New Hadamard-type inequalities for functions whose derivatives are (α,m)-convex functions

Abstract

In this paper some new inequalities are proved related to left hand side of Hermite-Hadamard inequality for the classes of functions whose derivatives of absolute values are (α,m)-convex.

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New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

Abstract

We derive some Hermite Hamamard type integral inequalities for functions whose second derivatives absolute value are convex. Some eror estimates for the trapezoidal formula are obtained. Finally, some natural applications to special means of real numbers are given

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