论文信息 - Strongly convex functions of higher order - 字舞流文

Strongly convex functions of higher order

Abstract The notion of strongly n -convex functions with modulus c > 0 is introduced and investigated. Relationships between such functions and n -convex functions in the sense of Popoviciu as well as generalized convex functions in the sense of Beckenbach are given. Characterizations by derivatives are presented. Some results on strongly Jensen n -convex functions are also given.

Roman Ger | Kazimierz Nikodem | R. Ger | K. Nikodem

[1] E. Polovinkin. Strongly convex analysis , 1996 .

[2] S. Wa̧sowicz. Support-type properties of convex functions of higher order and Hadamard-type inequalities , 2007, 0807.4103.

[3] J. Hiriart-Urruty,et al. Fundamentals of Convex Analysis , 2004 .

[4] Z. Ciesielski. Some properties of convex functions of higher orders , 1959 .

[5] ON n-PARAMETER FAMILIES OF FUNCTIONS AND ASSOCIATED CONVEX FUNCTIONS , 1950 .

[6] A. Pinkus,et al. Extending n-convex functions , 2005 .

[7] Z. Páles,et al. On convex functions of higher order , 2008 .

[8] Z. Páles,et al. Generalized convexity and separation theorems , 2007 .

[9] Tibère Popoviciu,et al. Les fonctions convexes , 1944 .

[10] Kazimierz Nikodem,et al. ON STRONGLY MIDCONVEX FUNCTIONS , 2011 .

[11] Z. Páles,et al. Hadamard-type inequalities for generalized convex functions , 2003 .

[12] Convex functions of higher orders in Euclidean spaces , 1972 .

[13] Some properties of generalized higher-order convexity , 2008, 0807.4126.

[14] E. Beckenbach,et al. On generalized convex functions , 1945 .

[15] n-convex functions in linear spaces , 1974 .

[16] D. Varberg. Convex Functions , 1973 .

[17] Zsolt Páles,et al. CHARACTERIZATIONS OF INNER PRODUCT SPACES BY STRONGLY CONVEX FUNCTIONS , 2011 .

[18] Attila Gilányi,et al. An Introduction to the Theory of Functional Equations and Inequalities , 2008 .

[19] N. Merentes,et al. Remarks on strongly convex functions , 2010 .