A Generalization of m-Convexity and a Sandwich Theorem

Lara, Teodoro; Matkowski, Janusz; Merentes, Nelson; Quintero, Roy; Wróbel, Małgorzata

doi:10.1515/amsil-2017-0003

Abstract

Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.

References

[1] Aczél J., Ng C.T., A lemma on the angles between a fixed line and the lines connecting a fixed point on it with the points of a convex arc, Internat. Ser. Numer. Math. 103 (1992), 463-464.10.1007/978-3-0348-7565-3_40
Search in Google Scholar Back to article
[2] Aumann G., Konvexe Funktionen und Induktion bei Ungleichungen zwischen Mittelverten, S.-B. math.-naturw. Abt. Bayer. Akad. Wiss. München 1933, pp. 405-413.
Search in Google Scholar Back to article
[3] Baron K., Matkowski J., Nikodem K., A sandwich with convexity, Math. Pannonica 5 (1994), no. 1, 139-144.
Search in Google Scholar Back to article
[4] Daróczy Z., Páles Zs., Convexity with given infinite weight sequences, Stochastica 11 (1987), 5-12.
Search in Google Scholar Back to article
[5] Dragomir S.S., Toader G.H., Some inequalities for m-convex functions, Studia Univ. Babes-Bolyai Math. 38 (1993), no. 1, 21-28.
Search in Google Scholar Back to article
[6] Kuczma M., An introduction to the theory of functional equations and inequalities, Cauchy’s equation and Jensen’s inequality, Panstwowe Wydawnictwo Naukowe and Uniwersytet Slaski, Warszawa-Kraków-Katowice, 1985; Second edition (edited by A. Gilányi), Birkhäuser, Basel, 2008.10.1007/978-3-7643-8749-5
Search in Google Scholar Back to article
[7] Lara T., Sánchez J.L., Rosales E., New properties of m-convex functions, Internat. J. Math. Anal. 9 (2015), no. 15, 735-742.
Search in Google Scholar Back to article
[8] Lara T., Merentes N., Quintero R., Rosales E., On strongly m-convex functions, Math. Aeterna 5 (2015), no. 3, 521-535.
Search in Google Scholar Back to article
[9] Matkowski J., A functional inequality characterizing convex functions, conjugacy and a generalization of Hölder’s and Minkowski’s inequalities, Aequationes Math. 40 (1990), 169-180.10.1007/BF02112293
Search in Google Scholar Back to article
[10] Matkowski J., Lp-like paranorms, in: Selected topics in functional equations and iteration theory, Proceedings of the Austrian-Polish Seminar, Universität Graz, October 24-26, 1991 (edited by D. Gronau, L. Reich), Grazer Math. Ber., 316, Karl-Franzens- Univ. Graz, Graz, 1992, pp. 103-139.
Search in Google Scholar Back to article
[11] Matkowski J., Pycia M., Convex-like inequality, homogeneity, subadditivity, and a characterization of Lp-norm, Ann. Polon. Math. 60 (1995), 221-230.10.4064/ap-60-3-221-230
Search in Google Scholar Back to article
[12] Matkowski J., Wróbel M., Remark on m-convexity and sandwich theorem, J. Math. Anal. Appl. 451 (2017), 924-930.10.1016/j.jmaa.2017.02.041
Search in Google Scholar Back to article
[13] Mocanu P.T., Serb I., Toader G.H., Real star-convex functions, Studia Univ. Babes- Bolyai Math. 42 (1997), no. 3, 65-80.
Search in Google Scholar Back to article
[14] Pycia M., Linear functional inequalities - a general theory and new special cases, Dissertationes Math. 438 (2006), 62 pp.10.4064/dm438-0-1
Search in Google Scholar Back to article
[15] Toader G.H., Some generalizations of the convexity, Proc. Colloq. Approx. Optim. Cluj-Napoca (Romania) 1984, pp. 329-338.
Search in Google Scholar Back to article
[16] Toader S., The order of a star-convex function, Bull. Appl. Comp. Math. 85 (1998), 347-350.
Search in Google Scholar Back to article

A Generalization of m-Convexity and a Sandwich Theorem

Abstract

Paradigm

My account