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Improvement of Jensen's inequality for superquadratic functions (CROSBI ID 163341)

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Abramovich, Shoshana ; Ivanković, Božidar ; Pečarić, Josip Improvement of Jensen's inequality for superquadratic functions // The Australian journal of mathematical analysis and applications, 7 (2010), 1; 1-15

Podaci o odgovornosti

Abramovich, Shoshana ; Ivanković, Božidar ; Pečarić, Josip

engleski

Improvement of Jensen's inequality for superquadratic functions

Since 1907, the famous Jensen's inequality has been refined in different manners. In our paper, we refine it applying superquadratic functions and separations of domains for convex functions. There are convex functions which are not superquadratic and superquadratic functions which are not convex. For superquadratic functions which are not convex we get inequalities analogue to inequalities satisfied by convex functions. For superquadratic functions which are convex (including many useful functions) we get refinements of Jensen's inequality and its extensions.

Convex functions; Jensen's inequality; Superquadratic functions

Article 14

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Podaci o izdanju

7 (1)

2010.

1-15

objavljeno

1449-5910

Povezanost rada

Matematika

Poveznice
Indeksiranost