论文信息 - Remarks on strongly convex functions

Remarks on strongly convex functions

Some properties of strongly convex functions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers–Ulam stability result for strongly convex functions are given. An integral Jensen-type inequality and a Hermite–Hadamard-type inequality for strongly convex functions are obtained. Finally, a relationship between strong convexity and generalized convexity in the sense of Beckenbach is shown.

N. Merentes | Kazimierz Nikodem | K. Nikodem

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

[2] S. M. Ulam,et al. Approximately convex functions , 1952 .

[3] M. Mehdi,et al. On Convex Functions , 1964 .

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

[5] A sandwich with convexity. , 1994 .

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

[7] Charles E. M. Pearce,et al. Selected Topics on Hermite-Hadamard Inequalities and Applications , 2003 .

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

[9] Constantin P. Niculescu,et al. Convex Functions and Their Applications: A Contemporary Approach , 2005 .

[10] Z. Páles,et al. Characterizations of convexity via Hadamard's inequality , 2006 .

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

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