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 Cauchy-type means for positive linear functionals

2011 ◽  
Vol 42 (4) ◽  
pp. 511-530
Author(s):  
M. Anwar ◽  
J. Pecaric ◽  
M. Rodi´c Lipanovi´c
Keyword(s):  
Jensen’S Inequality ◽  
Integral Form ◽  
Mean Value ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Discrete Form ◽  
Mean Value Theorems ◽  
Positive Linear Functionals

Some mean-value theorems of the Cauchy type, which are connected with Jensen's inequality, are given in \cite{Mercer2} in discrete form and in \cite{PPSri} in integral form. Here we give the generalization of that result for positive linear functionals. Using that result, new means of Cauchy type for positive linear functionals are given. Monotonicity of these new means is also discussed.

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 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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