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Rajba, Teresa

A generalization of multiple Wright-convex functions via randomization. (English) Zbl 1241.26010

J. Math. Anal. Appl. 388, No. 1, 548-565 (2012).
The author considers a general class of nonnegative real functions, which are generalizations of \(n\)-Wright-convex functions introduced by A. Gilányi and Zs. Páles [Math. Inequal. Appl. 11, No. 2, 271–282 (2008; Zbl 1141.26304)], and studied also by Gy. Maksa and Zs. Páles [J. Math. Anal. Appl. 359, No. 2, 439–443 (2009; Zbl 1175.26027)]. Series and integral representations, along with many consequences are proved. The results are, however, too complicated to be presented here.
Reviewer: József Sándor (Cluj-Napoca)

Cited in 2 Documents

MSC:

26B25 Convexity of real functions of several variables, generalizations
26D20 Other analytical inequalities
26D99 Inequalities in real analysis
26B35 Special properties of functions of several variables, Hölder conditions, etc.

Keywords:

convexity; higher-order convexity; multiple monotone function; higher-order Wright-convexity; completely monotone function; difference operator

Citations:

Zbl 1141.26304; Zbl 1175.26027
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\textit{T. Rajba}, J. Math. Anal. Appl. 388, No. 1, 548--565 (2012; Zbl 1241.26010)
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References:

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