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 The Applications of Functional Variants of Jensen's Inequality

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Zlatko Pavić
Keyword(s):  
Convex Functions ◽  
Functional Form ◽  
Jensen’S Inequality ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Positive Linear Functionals ◽  
Functional Variants ◽  
Several Variables

The paper is inspired by McShane's results on the functional form of Jensen's inequality for convex functions of several variables. The work is focused on applications and generalizations of this important result. At that, the generalizations of Jensen's inequality are obtained using the positive linear functionals.

scholarly journals Application of Functionals in Creating Inequalities

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Zlatko Pavić ◽  
Shanhe Wu ◽  
Vedran Novoselac
Keyword(s):  
Convex Functions ◽  
Functional Form ◽  
Closed Interval ◽  
Jensen’S Inequality ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Hadamard Inequality ◽  
Positive Linear Functionals ◽  
Main Inequality

The paper deals with the fundamental inequalities for convex functions in the bounded closed interval. The main inequality includes convex functions and positive linear functionals extending and refining the functional form of Jensen’s inequality. This inequality implies the Jensen, Fejér, and, thus, Hermite-Hadamard inequality, as well as their refinements.

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.

scholarly journals Functions Like Convex Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Zlatko Pavić
Keyword(s):  
Convex Functions ◽  
Convex Sets ◽  
Jensen’S Inequality ◽  
Convexity Property ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Positive Linear Functionals ◽  
Functional Forms ◽  
Common Center ◽  
The Common

The paper deals with convex sets, functions satisfying the global convexity property, and positive linear functionals. Jensen's type inequalities can be obtained by using convex combinations with the common center. Following the idea of the common center, the functional forms of Jensen's inequality are considered in this paper.

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

A mean-value theorem for positive linear functionals

2019 ◽  
Vol 189 (4) ◽  
pp. 675-681
Author(s):  
Mircea Ivan ◽  
Vicuta Neagos ◽  
Andra-Gabriela Silaghi
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Linear Functionals ◽  
Positive Linear Functionals

scholarly journals Cauchy type means for some generalized convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Naila Mehreen ◽  
Matloob Anwar
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Cauchy Type ◽  
Jensen's Inequality ◽  
Generalized Convex Functions

AbstractIn this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense. Also, by using Hermite–Hadamard inequalities for the respective generalized convex functions, we find new generalized Cauchy type means.

scholarly journals Cauchy-type means for positive linear functionals

2011 ◽  
Vol 42 (4) ◽  
Author(s):  
M. Anwar ◽  
J. Pecaric ◽  
M. Rodi´c Lipanovi´c
Keyword(s):  
Cauchy Type ◽  
Linear Functionals ◽  
Positive Linear Functionals

Cyclic refinements of the discrete and integral form of Jensen’s inequality with applications

Analysis ◽  
2016 ◽  
Vol 36 (4) ◽  
Author(s):  
László Horváth ◽  
Khuram Ali Khan ◽  
Josip Pečarić
Keyword(s):  
Jensen’S Inequality ◽  
Integral Form ◽  
Jensen's Inequality ◽  
Weighted Version

AbstractIn this paper we introduce new refinements of both the discrete and the classical Jensen’s inequality. First, we give the weighted version of a recent cyclic refinement. By using this result, we obtain new refinements of the classical Jensen’s inequality. We investigate

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