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.

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.

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 A family of the Cauchy type mean-value theorems

2005 ◽  
Vol 306 (2) ◽  
pp. 730-739 ◽  
Author(s):  
Josip E. Pečarić ◽  
Ivan Perić ◽  
H.M. Srivastava
Keyword(s):  
Mean Value ◽  
Cauchy Type ◽  
Mean Value Theorems

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.

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