Exponential Convexity Induced by Steffensen’s Inequality and Positive Measures

2018 ◽  
Vol 73 (4) ◽  
Author(s):  
Julije Jakšetić ◽  
Josip Pečarić ◽  
Ksenija Smoljak Kalamir
Keyword(s):  
Exponential Convexity ◽  
Steffensen’S Inequality

scholarly journals Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators

2021 ◽  
Vol 45 (5) ◽  
pp. 797-813
Author(s):  
SAJID IQBAL ◽  
◽  
GHULAM FARID ◽  
JOSIP PEČARIĆ ◽  
ARTION KASHURI
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Liouville Fractional Derivative ◽  
Fractional Derivative Operators

In this paper we present variety of Hardy-type inequalities and their refinements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modified extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

scholarly journals Generalizations of Steffensen’s inequality by Lidstone’s polynomial and related results

2019 ◽  
Vol 43 (3) ◽  
pp. 293-307
Author(s):  
Josip Pečarić ◽  
Anamarija Perušić Pribanić ◽  
Ana Vukelić
Keyword(s):  
Steffensen’S Inequality

Multidimensional reversed Hardy type inequalities for monotone functions

2014 ◽  
Vol 07 (04) ◽  
pp. 1450055
Author(s):  
Saad Ihsan Butt ◽  
Josip Pečarić ◽  
Ivan Perić ◽  
Marjan Praljak
Keyword(s):  
Mean Value ◽  
Monotone Functions ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Multidimensional Generalization ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Cauchy Means

In this paper, we will give some multidimensional generalization of reversed Hardy type inequalities for monotone functions. Moreover, we will give n-exponential convexity, exponential convexity and related results for some functionals obtained from the differences of these inequalities. At the end we will give mean value theorems and Cauchy means for these functionals.

scholarly journals On an extension of Hölder's inequality

1995 ◽  
Vol 51 (3) ◽  
pp. 453-458 ◽  
Author(s):  
C.E.M. Pearce ◽  
J. Peĉarić
Keyword(s):  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Steffensen’S Inequality

An new extension of Hölder's inequality is derived. This is shown to follow from a generalisation of Steffensen's inequality.

Steffensen’s Inequality

1993 ◽  
pp. 311-332
Author(s):  
D. S. Mitrinović ◽  
J. E. Pečarić ◽  
A. M. Fink
Keyword(s):  
Steffensen’S Inequality
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