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2021 | 35 (2) | 250--259
Tytuł artykułu

Sandwich Type Results for m-Convex Real Functions

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.(original abstract)
Rocznik
Tom
Strony
250--259
Opis fizyczny
Twórcy
autor
  • University of the Andes, Venezuela
  • University of the Andes, Venezuela
Bibliografia
  • Baron, J. Matkowski, and K. Nikodem, A sandwich with convexity, Math. Pannon. 5 1994, no. 1, 139-144. K.
  • Bracamonte M., Giménez J., and Medina J., Sandwich theorem for reciprocally strongly convex functions, Rev. Colombiana Mat. 52 2018, no. 2, 171-184.
  • Kuczma, M. An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality, Second edition, Birkhäuser Verlag, Basel, 2009.
  • Lara T., Matkowski J., Merentes N., Quintero R., and M. Wróbel, A generalization of m-convexity and a sandwich theorem, Ann. Math. Sil. 31 2017, 107-126.
  • Lara T., Merentes N., Páles Z., Quintero R., and Rosales E., On m-convexity on real linear spaces, UPI Journal of Mathematics and Biostatistics 1 2018, no. 2, JMB8, 16 pp.
  • Lara T., Merentes N., Quintero R., and Rosales E., On m-concave functions on real linear spaces, Bol. Asoc. Mat. Venez. 23 2016, no. 2, 131-137.
  • Lara T., Merentes N., Quintero R., and Rosales E., On m-convexity of set-valued functions, Adv. Oper. Theory 4 2019, no. 4, 767-783.
  • Lara T., Merentes N., Rosales E., and Tineo A., Properties and characterizations of convex functions on time scales, Ann. Math. Sil. 32 2018, 237-245.
  • Lara T. and Rosales E., Strongly convex functions on time scales, UPI Journal of Mathematics and Biostatistics 1 2018, no. 2, JMB9, 10 pp.
  • Lara T. and Rosales E., Log m-convex functions, Moroc. J. of Pure and Appl. Anal. (MJPAA) 5 2019, no. 2, 117-124.
  • Lara T., Rosales E., and Sánchez J.L., New properties of m-convex functions, Int. J. Math. Anal. (Ruse) 9 2015, no. 15, 735-742.
  • Matkowski J. and Wróbel M., Sandwich theorem for m-convex functions, J. Math. Anal. Appl. 451 2017, no. 2, 924-930.
  • Merentes N. and Nikodem K., Remarks on strongly convex functions, Aequationes. Math. 80 2010, no. 1-2, 193-199.
  • Niculescu C.P. and Persson L.-E., Convex Functions and Their Applications. A Contemporary Approach, CMS Books in Mathematics, 23, Springer, New York, 2006.
  • Nikodem K. and Wasowicz S., A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math. 49 1995, no. 1-2, 160-164.
  • Olbrys A., On separation by h-convex functions, Tatra Mt. Math. Publ. 62 2015, 105-111.
  • Roberts A.W. and Varberg D.E., Convex Functions, Pure and Applied Mathematics, 57, Academic Press, New York, 1973.
  • Sadowska E., A sandwich with convexity for set-valued functions, Math. Pannon. 7 1996, no. 1, 163-169.
  • Toader G., 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.
  • Toader G., On a generalization of the convexity, Mathematica (Cluj) 30(53) 1988, no. 1, 83-87.
  • Valentine F.A., Convex Sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York, 1964.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171629074

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