scholarly journals Some inequalities for weighted and integral means of convex functions on linear spaces

2020 ◽  
Vol 2 (2) ◽  
pp. 197-209
Author(s):  
SILVESTRU SEVER DRAGOMIR
Keyword(s):  
Convex Functions ◽  
Integral Means ◽  
Linear Spaces

scholarly journals The differentiability of convex functions on topological linear spaces

1990 ◽  
Vol 42 (2) ◽  
pp. 201-213 ◽  
Author(s):  
Bernice Sharp
Keyword(s):  
Convex Functions ◽  
Inductive Limit ◽  
Asplund Space ◽  
Fréchet Spaces ◽  
Linear Spaces ◽  
Asplund Spaces ◽  
Continuous Convex Function ◽  
Mazur’S Theorem ◽  
Topological Linear ◽  
Differentiability Properties

In this paper topological linear spaces are categorised according to the differentiability properties of their continuous convex functions. Mazur's Theorem for Banach spaces is generalised: all separable Baire topological linear spaces are weak Asplund. A class of spaces is given for which Gateaux and Fréchet differentiability of a continuous convex function coincide, which with Mazur's theorem, implies that all Montel Fréchet spaces are Asplund spaces. The effect of weakening the topology of a given space is studied in terms of the space's classification. Any topological linear space with its weak topology is an Asplund space; at the opposite end of the topological spectrum, an example is given of the inductive limit of Asplund spaces which is not even a Gateaux differentiability space.

scholarly journals INEQUALITIES IN TERMS OF THE GÂTEAUX DERIVATIVES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

2011 ◽  
Vol 83 (3) ◽  
pp. 500-517 ◽  
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Linear Spaces ◽  
Divergence Measures ◽  
Gateaux Derivatives ◽  
Gâteaux Derivatives

AbstractSome inequalities in terms of the Gâteaux derivatives related to Jensen’s inequality for convex functions defined on linear spaces are given. Applications for norms, mean f-deviations and f-divergence measures are provided as well.

scholarly journals On some weighted integral inequalities for convex functions related to Fejér’s result

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 195-218
Author(s):  
K.L. Tseng ◽  
Shiow-Ru Hwang ◽  
S.S. Dragomir
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Means ◽  
Weighted Integral

In this paper, we introduce some functionals associated with weighted integral means for convex functions. Some new Fej?r-type inequalities are obtained as well.

scholarly journals Bounds for the normalised Jensen functional

2006 ◽  
Vol 74 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Sever S. Dragomir
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Normed Spaces ◽  
Jensen's Inequality ◽  
Linear Spaces ◽  
Leibler Divergence ◽  
Jensen Functional ◽  
New Inequalities

New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen's inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon's inequality and the positivity of Kullback-Leibler divergence are obtained.

scholarly journals The integral means of close-to-convex functions.

1972 ◽  
Vol 19 (4) ◽  
pp. 377-379 ◽  
Author(s):  
Donald R. Wilken
Keyword(s):  
Convex Functions ◽  
Integral Means

The FM and BCQ Qualifications for Inequality Systems of Convex Functions in Normed Linear Spaces

2021 ◽  
Vol 31 (2) ◽  
pp. 1410-1432
Author(s):  
Chong Li ◽  
Kung Fu Ng ◽  
Jen-Chih Yao ◽  
Xiaopeng Zhao
Keyword(s):  
Convex Functions ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Inequality Systems
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