scholarly journals Inequalities of the Edmundson-Lah-Ribarč type for n-convex functions with applications

2021 ◽  
Vol 73 (1) ◽  
pp. 89-106
Author(s):  
R. Mikić ◽  
D. Pečarić ◽  
J. Pečarić
Keyword(s):  
Convex Functions ◽  
Linear Functionals ◽  
Positive Linear Functionals

UDC 517.5 We derive some Edmundson – Lah – Ribarič type inequalities for positive linear functionals and -convex functions. Main results are applied to the generalized -divergence functional. Examples with Zipf – Mandelbrot law are used to illustrate the results.

INEQUALITIES OF JENSEN’S TYPE FOR POSITIVE LINEAR FUNCTIONALS ON HERMITIAN UNITAL BANACH -ALGEBRAS

2020 ◽  
Vol 102 (2) ◽  
pp. 308-318
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Convex Functions ◽  
Banach Algebras ◽  
General Setting ◽  
Linear Functionals ◽  
Positive Linear Functionals ◽  
Hermitian Unital

We establish inequalities of Jensen’s and Slater’s type in the general setting of a Hermitian unital Banach $\ast$-algebra, analytic convex functions and positive normalised linear functionals.

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 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.

Interval oscillation criteria for self-adjoint matrix Hamiltonian systems

2005 ◽  
Vol 135 (5) ◽  
pp. 1085-1108 ◽  
Author(s):  
Qigui Yang ◽  
Yun Tang
Keyword(s):  
Hamiltonian Systems ◽  
Half Line ◽  
Linear Functionals ◽  
Matrix Space ◽  
Differential Systems ◽  
Adjoint Matrix ◽  
Oscillation Criteria ◽  
Positive Linear Functionals ◽  
Interval Oscillation ◽  
New Criteria

By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such as

Refinements of the majorization-type inequalities via green and fink identities and related results

2018 ◽  
Vol 68 (4) ◽  
pp. 773-788 ◽  
Author(s):  
Sadia Khalid ◽  
Josip Pečarić ◽  
Ana Vukelić
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Ostrowski’S Inequality ◽  
New Family ◽  
Exponentially Convex Functions ◽  
The Difference

Abstract In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

On the approximation of convex functions using linear positive operators

2017 ◽  
Vol 26 (2) ◽  
pp. 137-143
Author(s):  
DAN BARBOSU
Keyword(s):  
Convex Functions ◽  
Remainder Term ◽  
Mean Value ◽  
Positive Operators ◽  
Linear Functionals ◽  
Linear Positive Operators ◽  
Famous Theorem ◽  
Approximation Formulas ◽  
Phd Thesis ◽  
Higher Order Convexity

The goal of the paper is to present some results concerning the approximation of convex functions by linear positive operators. First, one recalls some results concerning the univariate real valued convex functions. Next, one presents the notion of higher order convexity introduced by Popoviciu [Popoviciu, T., Sur quelques propri´et´ees des fonctions d’une ou deux variable r´eelles, PhD Thesis, La Faculte des Sciences de Paris, 1933 (June)] . The Popoviciu’s famous theorem for the representation of linear functionals associated to convex functions of m−th order (with the proof of author) is also presented. Finally, applications of the convexity to study the monotonicity of sequences of some linear positive operators and also mean value theorems for the remainder term of some approximation formulas based on linear positive operators are presented.

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