A Generalization of m-Convexity and a Sandwich Theorem

• Autorzy: Teodoro Lara , Janusz Matkowski , Nelson Merentes , Roy Quintero , Małgorzata Wróbel
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Mathematics; Mathematical functions; Mathematical inequalities; Linear equation

PL

Matematyka; Funkcje matematyczne; Nierówności matematyczne; Równania liniowe

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2017
• Tom: 31
• Strony: 107--126

Twórcy

autor

Teodoro Lara

• University of the Andes, Venezuela

autor

Janusz Matkowski

• University of Zielona Gora, Poland

autor

Nelson Merentes

• The Central University of Venezuela, Venezuela

autor

Roy Quintero

• The Central University of Venezuela, Venezuela

autor

Małgorzata Wróbel

• Politechnika Częstochowska

Bibliografia

• 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.
• Aumann G., Konvexe Funktionen und Induktion bei Ungleichungen zwischen Mittelverten, S.-B. math.-naturw. Abt. Bayer. Akad. Wiss. München 1933, pp. 405-413.
• Baron K., Matkowski J., Nikodem K., A sandwich with convexity, Math. Pannonica 5 (1994), no. 1, 139-144.
• Daróczy Z., Páles Zs., Convexity with given infinite weight sequences, Stochastica 11 (1987), 5-12.
• Dragomir S.S., Toader G.H., Some inequalities for m-convex functions, Studia Univ. Babes-Bolyai Math. 38 (1993), no. 1, 21-28.
• 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.
• Lara T., Sánchez J.L., Rosales E., New properties of m-convex functions, Internat. J. Math. Anal. 9 (2015), no. 15, 735-742.
• Lara T., Merentes N., Quintero R., Rosales E., On strongly m-convex functions, Math. Aeterna 5 (2015), no. 3, 521-535.
• 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.
• 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.
• Matkowski J., Pycia M., Convex-like inequality, homogeneity, subadditivity, and a characterization of Lp-norm, Ann. Polon. Math. 60 (1995), 221-230.
• Matkowski J., Wróbel M., Remark on m-convexity and sandwich theorem, J. Math. Anal. Appl. 451 (2017), 924-930.
• Mocanu P.T., Serb I., Toader G.H., Real star-convex functions, Studia Univ. Babes- Bolyai Math. 42 (1997), no. 3, 65-80.
• Pycia M., Linear functional inequalities - a general theory and new special cases, Dissertationes Math. 438 (2006), 62 pp.
• Toader G.H., Some generalizations of the convexity, Proc. Colloq. Approx. Optim. Cluj-Napoca (Romania) 1984, pp. 329-338.
• Toader S., The order of a star-convex function, Bull. Appl. Comp. Math. 85 (1998), 347-350.

Identyfikatory

DOI

10.1515/amsil-2017-0003