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 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.

Two-sided Hardy-type inequalities for monotone functions

2010 ◽  
Vol 55 (8-10) ◽  
pp. 973-989 ◽  
Author(s):  
Lars-Erik Persson ◽  
Olga V. Popova ◽  
Vladimir D. Stepanov
Keyword(s):  
Monotone Functions ◽  
Hardy Type Inequalities ◽  
Hardy Type

Two-sided hardy-type inequalities for monotone functions

2009 ◽  
Vol 80 (3) ◽  
pp. 814-817 ◽  
Author(s):  
V. D. Stepanov ◽  
L. E. Persson ◽  
O. V. Popova
Keyword(s):  
Monotone Functions ◽  
Hardy Type Inequalities ◽  
Hardy Type

scholarly journals Mean-value theorems and some symmetric means

2013 ◽  
Vol 46 (3) ◽  
Author(s):  
Janusz Matkowski
Keyword(s):  
Mean Value ◽  
Mean Value Theorems ◽  
Cauchy Means

AbstractSome variants of the Lagrange and Cauchy mean-value theorems lead to the conclusion that means, in general, are not symmetric. They are symmetric iff they coincide (respectively) with the Lagrange and Cauchy means. Under some regularity assumptions, we determine the form of all the relevant symmetric means.

scholarly journals A generation method for completely monotone functions

2019 ◽  
Vol 13 (3) ◽  
pp. 883-894
Author(s):  
Julije Jaksetic
Keyword(s):  
Mean Value ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Monotone Functions ◽  
Completely Monotone Functions ◽  
Mean Value Theorems ◽  
Monotonicity Properties ◽  
Completely Monotone ◽  
Present Technique

In this article we present technique how to produce completely monotone functions using linear functionals and already known families of completely monotone functions. After that, using mean value theorems, we construct means of Cauchy type that have monotonicity properties.

Mean Value Theorems and Linear Operators

1955 ◽  
Vol 62 (4) ◽  
pp. 217 ◽  
Author(s):  
Philip Hartman ◽  
Aurel Wintner
Keyword(s):  
Mean Value ◽  
Linear Operators ◽  
Mean Value Theorems

scholarly journals Some new Hardy-type inequalities on time scales

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmed A. El-Deeb ◽  
Hamza A. Elsennary ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hardy Type Inequalities ◽  
Hardy Type
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