On (M, N)-convex functions

József Sándor and Edith Egri
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 4, Pages 40–47
Full paper (PDF, 168 Kb)

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Authors and affiliations

József Sándor
Babes–Bolyai University, Department of Mathematics,
Cluj-Napoca, Romania

Edith Egri
Babes–Bolyai University, Department of Mathematics,
Cluj-Napoca, Romania

Abstract

We consider certain properties of functions f : J → I (I, J intervals) such that
f(M(x, y)) ≤ N(f(x), f(y)), where M and N are general means. Some results are extensions of the case M = N = L, where L is the logarithmic mean.

Keywords

• Mean
• Logarithmic mean
• Identric mean
• Integral mean
• Convex or concave functions with respect to a mean
• Subadditive functions
• Continuity

AMS Classification

• 26A51
• 26D99
• 39B72

References

 

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