m-Convex Functions of Higher Order

• Autorzy: Teodoro Lara , Nelson Merentes , Edgar Rosales
• Języki publikacji: EN

Abstrakty

EN

In this research we introduce the concept of m-convex function of higher order by means of the so called m-divided difference; elementary properties of this type of functions are exhibited and some examples are provided. (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Mathematical analysis

PL

Matematyka; Funkcje matematyczne; Analiza matematyczna

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2020
• Tom: 34 (2)
• Strony: 241--255

Twórcy

autor

Teodoro Lara

• University of the Andes, Venezuela

autor

Nelson Merentes

• The Central University of Venezuela, Venezuela

autor

Edgar Rosales

• University of the Andes, Venezuela

Bibliografia

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• R. Ger, Convex functions of higher orders in Euclidean spaces, Ann. Polon. Math. 25 (1972), 293-302.
• A. Gilányi and Z. Páles, On convex functions of higher order, Math. Inequal. Appl. 11 (2008), no. 2, 271-282.
• V. Janković, Divided differences, Teach. Math. 3 (2000), no. 2, 115-119.
• M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality, Second edition, Edited by A. Gilányi, Birkhäuser Verlag, Basel, 2009.
• T. Lara, N. Merentes, R. Quintero and E. Rosales, On strongly m-convex functions, Math. Æterna 5 (2015), no. 3, 521-535.
• T. Lara, R. Quintero, E. Rosales and J.L. Sánchez, On a generalization of the class of Jensen convex functions, Aequationes Math. 90 (2016), no. 3, 569-580.
• 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.
• N. Merentes and S. Rivas, The Develop of the Concept of Convex Function, XXVI Escuela Venezolana de Matemáticas, Mérida, Venezuela, 2013 (in Spanish).
• K. Nikodem, T. Rajba and S. Wąsowicz, On the classes of higher-order Jensen-convex functions and Wright-convex functions, J. Math. Anal. Appl. 396 (2012), no. 1, 261-269.
• T. Popoviciu, Sur quelques propriétés des fonctions d'une ou de deux variables réelles, Mathematica (Cluj) 8 (1934), 1-85.
• G. Toader, Some generalizations of the convexity, in: I. Marus˛ciac et al. (eds.), Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1985, pp. 329-338.

Identyfikatory

DOI

10.2478/amsil-2019-0013