Levinson type inequalities for higher order convex functions via Abel–Gontscharoff interpolation

Abstract

In this paper, Levinson type inequalities are studied for the class of higher order convex functions by using Abel-Gontscharoff interpolation. Cebyšev, Grüss, and Ostrowski-type new bounds are also found for the functionals involving data points of two types.

Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy

“…We further make con-nection of majorization with information theory and discuss our generalized majorization inequality in terms of divergences and entropies. The results we obtain in this paper are closely related to the contents given in [1][2][3][4][5]. Moreover, some related results with the present topic can also be found in [10,11,27,41,42].…”

Levinson-type inequalities via new Green functions and Montgomery identity

“…In [8], Adeel et al generalized Levinson's inequality for 3-convex functions; they also obtained some results for information theory. Similar results can be found in [9,10]. In [11], Witkowski showed the Levinson inequality with random variables.…”

Majorization inequalities via Green functions and Fink’s identity with applications to Shannon entropy

“…We further make connection of majorization with information theory and discuss our generalized majorization inequality in terms of divergences and entropies. The results we obtain in this paper are closely related to the contents of [1][2][3][4][5]. Moreover, some results related to the present topic can also be found in [19].…”

“…1 Department of Mathematics, Government College University, 38000 Faisalabad, Pakistan. 2 Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan. 3 Rudn University, Moscow, Russia.…”