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

Mean Value Theorems and Linear Operators

1955 ◽  
Vol 62 (4) ◽  
pp. 217-222 ◽  
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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