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
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 : JI (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

  1. Bullen, P. S. (2003) Handbook of means and their inequalities, Kluwer Acad. Publ.
  2. Matkowski, J. & J. R¨atz (1997) Convex functions wirh respect to an arbitrary mean, Intern. Ser. Num. Math., 123, 249–258.
  3. Matkowski, J. & J. R¨atz (1997) Convexity of the power functions wirh respect to symmetric homogeneous means, Intern. Ser. Num. Math., 123, 231–247.
  4. Matkowski, J. (2003) Affine and convex functions with respect to the logarithmic mean, Colloq. Math., 95, 217–230.
  5. Roberts, A. W. & D. E. Varberg (1973) Convex functions, Academic Press.
  6. Sándor, J. (1990) On the identric and logarithmic means, Aequationes Math., 40, 261–270.
  7. Sándor, J. (1998) Inequalities for generalized convex functions with applications, Babes–Bolyai Univ., Cluj, Romania (in Romanian).
  8. Sándor, J. & B. A. Bhayo (2015) On some some inequalities for the identric, logarithmic and related means, J. Math. Ineq., 9(3), 889–896.
  9. Zgraja, T. & Z. Kominek (1999) Convex functions wirh respect to logarithmic mean and sandwich theorem, Acta Univ. Car.–Math. Phys., 40(2), 75–78.
  10. 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

APA

Sándor, J., & Egri, E. (2015). On (M, N)-convex functions. Notes on Number Theory and Discrete Mathematics, 21(4), 40-47.

Chicago

Sándor, József, and Edith Egri. “On (M, N)-convex Functions.” Notes on Number Theory and Discrete Mathematics 21, no. 4 (2015): 40-47.

MLA

Sándor, József, and Edith Egri. “On (M, N)-convex Functions.” Notes on Number Theory and Discrete Mathematics 21.4 (2015): 40-47. Print.

Comments are closed.