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  • Author: Silvestru Sever Dragomir x
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Silvestru Sever Dragomir

Abstract

In this paper, some generalizations of Pompeiu's inequality for two complex-valued absolutely continuous functions are provided. They are applied to obtain some new Ostrowski type results. Reverses for the integral Cauchy-Bunyakovsky-Schwarz inequality are provided as well.

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Silvestru Sever Dragomir

Abstract

Perturbed companions of Ostrowski’s inequality for absolutely continuous functions whose derivatives are either bounded or of bounded variation and applications are given.

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Hamid Reza Moradi, Mohsen Erfanian Omidvar and Silvestru Sever Dragomir

Abstract

Some operator inequalities for synchronous functions that are related to the čebyšev inequality are given. Among other inequalities for synchronous functions it is shown that ∥ø(f(A)g(A)) - ø(f(A))ø(g(A))∥ ≤ max{║ø(f2(A)) - ø2(f(A))║, ║ø)G2(A)) - ø2(g(A))║} where A is a self-adjoint and compact operator on B(ℋ ), f, g ∈ C (sp (A)) continuous and non-negative functions and ø: B(ℋ ) → B(ℋ ) be a n-normalized bounded positive linear map. In addition, by using the concept of quadruple D-synchronous functions which is generalizes the concept of a pair of synchronous functions, we establish an inequality similar to čebyšev inequality.

Open access

Hamid Reza Moradi, Mohsen Erfanian Omidvar, Silvestru Sever Dragomir and Mohammad Saeed Khan

Abstract

In this paper by using the notion of sesquilinear form we introduce a new class of numerical range and numerical radius in normed space 𝒱, also its various characterizations are given. We apply our results to get some inequalities.