József Sándor and Edith Egri
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 4, Pages 40—47
Download full paper: PDF, 168 Kb
Details
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
- Bullen, P. S. (2003) Handbook of means and their inequalities, Kluwer Acad. Publ.
- Matkowski, J. & J. R¨atz (1997) Convex functions wirh respect to an arbitrary mean, Intern. Ser. Num. Math., 123, 249–258.
- Matkowski, J. & J. R¨atz (1997) Convexity of the power functions wirh respect to symmetric homogeneous means, Intern. Ser. Num. Math., 123, 231–247.
- Matkowski, J. (2003) Affine and convex functions with respect to the logarithmic mean, Colloq. Math., 95, 217–230.
- Roberts, A. W. & D. E. Varberg (1973) Convex functions, Academic Press.
- Sándor, J. (1990) On the identric and logarithmic means, Aequationes Math., 40, 261–270.
- Sándor, J. (1998) Inequalities for generalized convex functions with applications, Babes–Bolyai Univ., Cluj, Romania (in Romanian).
- Sándor, J. & B. A. Bhayo (2015) On some some inequalities for the identric, logarithmic and related means, J. Math. Ineq., 9(3), 889–896.
- Zgraja, T. & Z. Kominek (1999) Convex functions wirh respect to logarithmic mean and sandwich theorem, Acta Univ. Car.–Math. Phys., 40(2), 75–78.
- Zgraja, T. (2005) On continous convex or concave functions wirh respect to the logarithmic mean, Acta Univ. Car.–Math. Phys., 46(1), 3–10.
Related papers
Cite this paper
Sándor, J., & Egri, E. (2015). On (M, N)-convex functions. Notes on Number Theory and Discrete Mathematics, 21(4), 40-47.