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Chapter
Linear Inequalities via Interpolation Polynomials and Green Functions
Linear inequalities are those inequalities which involve linear functionals or linear relations. Its best examples are discrete and integral inequalities which are of great importance. In this book several gen...
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Chapter
Functions with Nondecreasing Increments
The main purpose of the present chapter is to establish the relationship of functions with nondecreasing increments (FWNDI) with other functions of high importance. Our special emphasis will be on the role of ...
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Book
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Chapter
Ostrowski Inequality
According to Hardy’s famous statement “Behind every theorem lies an inequality,” and it is true that many significant and well-known results in mathematics are inequalities, new types of interesting inequaliti...
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Chapter
Popoviciu and Čebyšev-Popoviciu Type Identities and Inequalities
The main aim of this section is to extend the definitions of ∇-convex and completely monotonic functions for two variables. We would construct some examples and applications of completely monotonic functions. ...
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Article
Open AccessWeighted averages of n-convex functions via extension of Montgomery’s identity
Using an extension of Montgomery’s identity and the Green’s function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum
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Article
Open AccessWeighted majorization inequalities for n-convex functions via extension of Montgomery identity using Green function
New identities and inequalities are given for weighted majorization theorem for n-convex functions by using extension of the Montgomery identity and Green function. Various bounds for the reminders in new general...
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Article
A Note on Generalized Mercer’s Inequality
We give an integral version and a refinement of M. Niezgoda’s extension of the variant of Jensen’s inequality given by A. McD. Mercer.
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Article
Open AccessGeneralized integral inequalities on time scales
The theory of dynamic equations on time scales which was formulated by Hilger is an area of mathematics which is currently receiving profuse attention. Despite the fact that the basic objective of times scales...
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Article
Measurements-based Moving Target Detection in Quantum Video
A method to detect a moving target in multi-channel quantum video is proposed based on multiple measurements on the video strip. The proposed method is capable of detecting the location of the moving target in...
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Article
Open AccessWeighted majorization theorems via generalization of Taylor’s formula
A new generalization of the weighted majorization theorem for n-convex functions is given, by using a generalization of Taylor’s formula. Bounds for the remainders in new majorization identities are given by usin...
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Article
Open AccessOn some inequalities for functions with nondecreasing increments of higher order
We investigate a class of functions with nondecreasing increments of higher order. A generalization of Brunk’s theorem is proved for that class of functions. Also, we consider functions with nondecreasing incr...
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Article
Open AccessExponential convexity for majorization
In this article, we give more generalized results than in Anwar et al. (2010) and Latif and Pečarić (2010) in new direction by using second-order divided difference. We investigate the exponential convexity an...
