Improvements of Some Inequalities via Steffensen-Popoviciu Measure and it’s Dual
الموضوعات : فصلنامه ریاضیSaeed Nazari Pasari 1 , Naser Abbasi 2 , Ali Barani 3
1 - Department of Mathematics, Faculty of Science, Lorestan University, 6815144316, Khoramabad, Iran.
2 - Department of Mathematics, Faculty of Science, Lorestan University, 6815144316, Khoramabad, Iran.
3 - Department of Mathematics, Faculty of Science, Lorestan University, 6815144316, Khoramabad, Iran.
الکلمات المفتاحية: Dual Steffensen-Popoviciu measure, Convex function, Strongly convex function, Coordinated concave.,
ملخص المقالة :
In this paper we establish new inequalities for convex and strongly convex defined on intervals in framework of Steffensen-Popoviciu and Dual Steffensen-Popoviciu measures are introduced. Some inequalities in this setting are also involved. Suitable examples are also involved are given.
[1] S.S. Dragomir, On the Hadamard’s inequlality for convex functions on the coordinates in a rectangle
from the plane, Taiwanese journal of mathematics, 2001 Dec 1:775-88.
[2] A.M. Fink, A best possible Hadamard inequality, Math. Inequal. Appl, 1998;1(2):223-30.
[3] J.B. Hiriart-Urruty, C. Lemarchal,Fundamentals of convex analysis, Springer Science & Business
Media, 2004.
[4] S. Nazari Pasari, A. Barani, N. Abbasi, Generalized integral Jensen inequality, Journal of Inequalities
and Applications, 2024 Feb 20;2024(1):25.
[5] C. P. Niculescu, On a result of G. Bennett, Bulletin mathmatique de la Socit des Sciences Mathmatiques de Roumanie, 2011 Jan 1:261-7.
[6] C. P. Niculescu, L. E. Persson, Convex functions and their applications, Vol. 23. New York: Springer,
2006.
[7] C. P. Niculescu, C. I. Spiridon, New Jensen-type inequalities, Journal of Mathematical Analysis and
Applications, 401(1), 343-348.
[8] C. P. Niculescu, M. M. Stanescu, The SteffensenPopoviciu measures in the context of quasiconvex
functions, J. Math. Inequal, 2017 Jun 1;11:469-83.
[9] J. Pecaric, F. Proschan, Y. L. Tong,Convex functions, partial orderings, and statistical applications,
Academic Press, Boston, 1982.
[10] B. T. Polyak,Existence theorems and convergence of minimizing sequences in extremum problems
with restrictions, Soviet Math. Dokl. 7, 7275, 1966
[11] T. Popoviciu, Notes sur les fonctions convexes d’ordre suprieur (IX), Bulletin Mathmatique de la
socit Roumaine des Sciences, 1941 Jan 1;43(1/2):85-141.
[12] A. W. Roberts, D. E. Varberg,Convex Functions, Academic Press, New York (1973)
[13] H. M. Srivastava, S. Mehrez, S. M. Sitnik, Hermite-Hadamard-type integral inequalities for convex
functions and their applications, Mathematics, 2022 Aug 31;10(17):3127.
