scholarly journals Some New Results Related to Favard's Inequality

2009 ◽  
Vol 2009 (1) ◽  
pp. 128486 ◽  
Author(s):  
Naveed Latif ◽  
J Pečarić ◽  
I Perić
Keyword(s):  
Favard’S Inequality

Favard’s inequality for pseudo-integral

2017 ◽  
Vol 11 (01) ◽  
pp. 1850015
Author(s):  
Bayaz Daraby ◽  
Hassan Ghazanfary Asll ◽  
Ildar Sadeqi
Keyword(s):  
Monotone Function ◽  
The Real ◽  
Favard’S Inequality

The purpose of this paper is to generalize Favard’s inequality for pseudo-integral. We consider two cases for the real semiring [Formula: see text], when pseudo-operations are defined by a continuous and monotone function and when the pseudo-addition is sup operation and the pseudo-multiplication is generated by a continuous and monotone function.

scholarly journals On Levinson's inequality involving averages of 3-convex functions

2020 ◽  
pp. 45-45
Author(s):  
Ana Vukelic
Keyword(s):  
Convex Functions ◽  
Divided Difference ◽  
Higher Order ◽  
Cauchy Type ◽  
Linear Functionals ◽  
New Family ◽  
Exponentially Convex Functions ◽  
Levinson’S Inequality ◽  
Favard’S Inequality ◽  
New Inequalities

By using the Levinson inequality we give the extension for 3-convex functions of Wulbert's result from Favard's Inequality on Average Values of Convex Functions, Math. Comput. Model. 37 (2003), 1383{1391. Also, we obtain inequalities with divided differences, and as a consequence, the convexity of higher order for function defined by divided difference is proved. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking at linear functionals associated with these new inequalities.

scholarly journals EXPONENTIAL CONVEXITY OF THE FAVARD'S INEQUALITY AND RELATED RESULTS

2017 ◽  
Vol 30 (1-2) ◽  
Author(s):  
Naveed Latif ◽  
Josip Pečarić ◽  
Ivan Perić
Keyword(s):  
Exponential Convexity ◽  
Favard’S Inequality

A b s t r a c t: In this paper we prove positive semi-definiteness of matrices generated by differences deduced from unweighted and weighted Favard's inequality. This implies a surprising property of exponential convexity of this differences which allows us to deduce Gram's, Lyapunov's and Dresher's types of inequalities for this differences.

Sign in / Sign up

Export Citation Format

Share Document