Sandwich Type Results For m-Convex Real Functions

Teodoro Lara; Edgar Rosales

doi:10.2478/amsil-2021-0006

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Sandwich Type Results For m-Convex Real Functions

Annales Mathematicae Silesianae

Volume 35 (2021): Issue 2 (September 2021)

By: Teodoro Lara and Edgar Rosales

Open Access

|May 2021

Abstract

We establish necessary and sufficient conditions allowing separation of pair of real functions by an m-convex and by an m-affine function. Some examples and a geometric interpretation of m-convexity of a function is exhibited, as well as a Jensen’s inequality for this kind of function.

References

[1] K. Baron, J. Matkowski, and K. Nikodem, A sandwich with convexity, Math. Pannon. 5 1994, no. 1, 139–144.
Search in Google Scholar Back to article
[2] M. Bracamonte, J. Giménez, and J. Medina, Sandwich theorem for reciprocally strongly convex functions, Rev. Colombiana Mat. 52 2018, no. 2, 171–184.10.15446/recolma.v52n2.77157
Search in Google Scholar Back to article
[3] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, Second edition, Birkhäuser Verlag, Basel, 2009.10.1007/978-3-7643-8749-5
Search in Google Scholar Back to article
[4] T. Lara, J. Matkowski, N. Merentes, R. Quintero, and M. Wróbel, A generalization of m-convexity and a sandwich theorem, Ann. Math. Sil. 31 2017, 107–126.10.1515/amsil-2017-0003
Search in Google Scholar Back to article
[5] T. Lara, N. Merentes, Z. Páles, R. Quintero, and E. Rosales, On m-convexity on real linear spaces, UPI Journal of Mathematics and Biostatistics 1 2018, no. 2, JMB8, 16 pp.
Search in Google Scholar Back to article
[6] T. Lara, N. Merentes, R. Quintero, and E. Rosales, On m-concave functions on real linear spaces, Bol. Asoc. Mat. Venez. 23 2016, no. 2, 131–137.
Search in Google Scholar Back to article
[7] T. Lara, N. Merentes, R. Quintero, and E. Rosales, On m-convexity of set-valued functions, Adv. Oper. Theory 4 2019, no. 4, 767–783.10.15352/aot.1810-1429
Search in Google Scholar Back to article
[8] T. Lara, N. Merentes, E. Rosales, and A. Tineo, Properties and characterizations of convex functions on time scales, Ann. Math. Sil. 32 2018, 237–245.10.1515/amsil-2017-0016
Search in Google Scholar Back to article
[9] T. Lara and E. Rosales, Strongly convex functions on time scales, UPI Journal of Mathematics and Biostatistics 1 2018, no. 2, JMB9, 10 pp.
Search in Google Scholar Back to article
[10] T. Lara and E. Rosales, Log m-convex functions, Moroc. J. of Pure and Appl. Anal. (MJPAA) 5 2019, no. 2, 117–124.10.2478/mjpaa-2019-0009
Search in Google Scholar Back to article
[11] T. Lara, E. Rosales, and J.L. Sánchez, New properties of m-convex functions, Int. J. Math. Anal. (Ruse) 9 2015, no. 15, 735–742.10.12988/ijma.2015.412389
Search in Google Scholar Back to article
[12] J. Matkowski and M. Wróbel, Sandwich theorem for m-convex functions, J. Math. Anal. Appl. 451 2017, no. 2, 924–930.10.1016/j.jmaa.2017.02.041
Search in Google Scholar Back to article
[13] N. Merentes and K. Nikodem, Remarks on strongly convex functions, Aequationes. Math. 80 2010, no. 1-2, 193–199.10.1007/s00010-010-0043-0
Search in Google Scholar Back to article
[14] C.P. Niculescu and L.-E. Persson, Convex Functions and Their Applications. A Contemporary Approach, CMS Books in Mathematics, 23, Springer, New York, 2006.10.1007/0-387-31077-0
Search in Google Scholar Back to article
[15] K. Nikodem and S. Wasowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math. 49 1995, no. 1-2, 160–164.10.1007/BF01827935
Search in Google Scholar Back to article
[16] A. Olbrys, On separation by h-convex functions, Tatra Mt. Math. Publ. 62 2015, 105–111.10.1515/tmmp-2015-0008
Search in Google Scholar Back to article
[17] A.W. Roberts and D.E. Varberg, Convex Functions, Pure and Applied Mathematics, 57, Academic Press, New York, 1973.
Search in Google Scholar Back to article
[18] E. Sadowska, A sandwich with convexity for set-valued functions, Math. Pannon. 7 1996, no. 1, 163–169.
Search in Google Scholar Back to article
[19] G. Toader, Some generalizations of the convexity, in: I. Murusciac and W.W. Breckner (eds.), Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj- Napoca, Cluj-Napoca, 1985, pp. 329–338.
Search in Google Scholar Back to article
[20] G. Toader, On a generalization of the convexity, Mathematica (Cluj) 30(53) 1988, no. 1, 83–87.
Search in Google Scholar Back to article
[21] F.A. Valentine, Convex Sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York, 1964.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/amsil-2021-0006 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 250 - 259

Submitted on: Oct 4, 2020

Accepted on: Apr 14, 2021

Published on: May 26, 2021

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

-convex function,

-affine function,

Jensen type inequality,

sandwich theorem

Related subjects:

Mathematics,

General mathematics

© 2021 Teodoro Lara, Edgar Rosales, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 35 (2021): Issue 2 (September 2021)