m-Convex Functions of Higher Order

Teodoro Lara 1 , Nelson Merentes 2 , and Edgar Rosales 1
  • 1 Departamento de Física y Matemáticas, Universidad de los Andes, Venezuela, Trujillo
  • 2 Escuela de matemáticas, Universidad Central de Venezuela, , Venezuela, Caracas


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.

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  • [1] S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math. 33 (2002), no. 1, 45–55.

  • [2] S.S. Dragomir and G. Toader, Some inequalities for m-convex functions, Studia Univ. Babeş-Bolyai Math. 38 (1993), no. 1, 21–28.

  • [3] R. Ger, Convex functions of higher orders in Euclidean spaces, Ann. Polon. Math. 25 (1972), 293–302.

  • [4] A. Gilányi and Z. Páles, On convex functions of higher order, Math. Inequal. Appl. 11 (2008), no. 2, 271–282.

  • [5] V. Janković, Divided differences, Teach. Math. 3 (2000), no. 2, 115–119.

  • [6] 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.

  • [7] T. Lara, N. Merentes, R. Quintero and E. Rosales, On strongly m-convex functions, Math. Æterna 5 (2015), no. 3, 521–535.

  • [8] 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.

  • [9] 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] N. Merentes and S. Rivas, The Develop of the Concept of Convex Function, XXVI Escuela Venezolana de Matemáticas, Mérida, Venezuela, 2013 (in Spanish).

  • [11] 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.

  • [12] T. Popoviciu, Sur quelques propriétés des fonctions d’une ou de deux variables réelles, Mathematica (Cluj) 8 (1934), 1–85.

  • [13] G. Toader, Some generalizations of the convexity, in: I. Maruşciac et al. (eds.), Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1985, pp. 329–338.


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