Naslov
General Linear Inequalities and Positivity. Higher order convexity

Autori
Khan, Asif R. ; Pečarić, Josip ; Praljak, Marjan ; Varošanec, Sanja

Vrsta, podvrsta i kategorija knjige
Autorske knjige, monografija, znanstvena

Izdavač
Element

Grad
Zagreb

Godina
2017

Stranica
271

ISBN
978-953-197-628-2

Ključne riječi
general linear inequality, convex function of higher order, $\nabla$ convex function, starshaped function, function with nondecreasing increments, the Montgomery identity, Lidstone polynomials, Hermite polynomials, Abel-Gontscharoff polynomials, the Fink identity, Čebyšev inequality, Ky-Fan inequality, mean value theorem, exponential convexity, linear functionals, mean
(general linear inequality, convex function of higher order, $\nabla$ convex function, starshaped function, function with nondecreasing increments, the Montgomery identity, Lidstone polynomials, Hermite polynomials, Abel-Gontscharoff polynomials, the Fink identity, Čebyšev inequality, Ky-Fan inequality, mean value theorem, exponential convexity, linear functionals, means)

Sažetak
The goal of this book is to present recent results on general linear inequalities in discrete and integral form with an emphasis on applications of higher order convexity. Namely, we investigate inequalities containing the sums or integrals of the form $\sum_i p_i f(x_i)$, $\sum_{; ; ; i, j}; ; ; p_{; ; ; ij}; ; ; f(x_i, y_j)$, $\int p(x) f(x) dx$ or similar for different classes of functions such as convex functions of higher order, $\nabla$-convex functions of higher order, starshaped functions, functions convex at a point etc. Using a concept of higher order convexity, we give necessary and sufficient conditions for positivity of the weighted averages of function values. From the obtained inequalities we construct new linear functionals as the differences of their left- hand and the right-hand sides, and study their properties. Corresponding mean value theorems and nontrivial classes of exponentially convex functions are given also. The book is organized in six chapters: 1. General Linear Inequalities for Sequences, 2. General Linear Inequalities for Functions of One Variable, 3. General Linear Inequalities for Multivariate Functions, 4. Functions with Nondecreasing Increments, 5. Linear Inequalities via Interpolation Polynomials, 6. Čebyšev-Popoviciu Type Inequalities.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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