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

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.

### 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.

### Citations:

Zbl 1141.26304; Zbl 1175.26027
Full Text:

### References:

 [1] Feller, W., Completely monotone functions and sequences, Duke math. J., 5, 661-674, (1939) · JFM 65.0473.03 [2] Gilányi, A.; Páles, Zs., On convex functions of higher order, Math. inequal. appl., 11, 2, 271-282, (2008) · Zbl 1141.26304 [3] E. Hopf, Über die Zusammenhänge zwischen gewissen höheren Differezenquotienten reeler Funktionen einer reelen Variablen und deren Defferzierbarkeitseigenschaften, Dissertation, Friedrich Wilhelms Universität, 1926. [4] Kuczma, M., An introduction to the theory of functional equations and inequalities, Pr. nauk. uniw. śl. katow., vol. 489, (1985), Państwowe Wydawnictwo Naukowe/Uniwersytet Śląski Warszawa/Kraków/Katowice [5] Niedbalska-Rajba, T., On decomposability semigroups on the real line, Colloq. math., 44, 347-348, (1981) · Zbl 0487.60022 [6] Maksa, Gy.; Páles, Zs., Decomposition of higher order wright-convex functions, J. math. anal. appl., 359, 2, 439-443, (2009) · Zbl 1175.26027 [7] Popoviciu, T., Sur quelques propriétés des fonctions dʼune ou de deux variables réelles, Mathematica (cluj), 8, 1-85, (1934) · JFM 60.0196.02 [8] Popoviciu, T., LES fonctions convexes, (1944), Hermann Paris · Zbl 0060.14911 [9] Roberts, A.W.; Varberg, D.E., Convex functions, Pure appl. math., vol. 57, (1973), Academic Press New York/London · Zbl 0289.26012 [10] Schwartz, L., Thèorie des distributions, (1966), Hermann Paris [11] Talvila, E., The regulated primitive integral, Illinois J. math., 53, 4, 1187-1219, (2009) · Zbl 1207.26018 [12] Widder, D.V., The Laplace transform, (1941), Princeton Univ. Press New Jersey · Zbl 0060.24801 [13] Williamson, R.E., Multiply monotone functions and their Laplace transforms, Duke math. J., 23, 189-207, (1956) · Zbl 0070.28501 [14] Wright, E.M., An inequality for convex function, Amer. math. monthly, 61, 620-622, (1954) · Zbl 0057.04801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.