scholarly journals Generalized Csiszár's f-divergence for Lipschitzian functions

2021 ◽  
pp. 13-30
Author(s):  
Đilda Pečarić ◽  
Josip Pečarić ◽  
Dora Pokaz
Keyword(s):  
Lipschitzian Functions

scholarly journals Some new integral inequalities for Lipschitzian functions

2018 ◽  
Vol 8 (2) ◽  
pp. 259-265 ◽  
Author(s):  
İmdat İşcan ◽  
Mahir Kadakal ◽  
Alper Aydın
Keyword(s):  
Lipschitz Class ◽  
Integral Inequalities ◽  
Lipschitzian Functions ◽  
Special Means ◽  
Different Types ◽  
New Type

This paper is about obtaining some new type of integral inequalities for functions from the Lipschitz class. For this, some new integral inequalities related to the differences between the two different types of integral averages for Lipschitzian functions are obtained. Moreover, applications for some special means as arithmetic, geometric, logarithmic, -logarithmic, harmonic, identric are given.

scholarly journals Sharp integral inequalities based on general Euler two-point formulae

2005 ◽  
Vol 46 (4) ◽  
pp. 555-574 ◽  
Author(s):  
J. Pečarić ◽  
I. Perić ◽  
A. Vukelić
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Functions Of Bounded Variation ◽  
Quadrature Formulae ◽  
Lipschitzian Functions ◽  
Integrable Functions

AbstractWe consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or R-integrable functions, are proved.

scholarly journals On Integral Inequalities Involving Generalized Lipschitzian Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Mohaemd Jleli ◽  
Bessem Samet
Keyword(s):  
Integral Inequalities ◽  
New Class ◽  
Lipschitzian Functions ◽  
Lipschitzian Mappings

A new class of mappings that includes the class of Lipschitzian mappings is introduced. For this kind of mappings, new integral inequalities of Hadamard’s type are obtained. Our results are extensions of many previous contributions related to integral inequalities for Lipschitzian mappings.

Directionally Lipschitzian Mappings on Baire Spaces

1984 ◽  
Vol 36 (1) ◽  
pp. 95-130 ◽  
Author(s):  
J. M. Borwein ◽  
H. M. Stròjwas
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Optimization Problems ◽  
Directional Derivatives ◽  
Primary Interest ◽  
Lipschitzian Functions ◽  
Lipschitzian Mappings ◽  
Generalized Directional Derivatives ◽  
Derivatives Of ◽  
Locally Convex

Studies of optimization problems have led in recent years to definitions of several types of generalized directional derivatives. Those derivatives of primary interest in this paper were introduced and investigated by F. M. Clarke ([5], [6], [7], [8]), J. B. Hiriart-Urruty ([12]), Lebourg ([16], [17]), R. T. Rockafellar ([23], [24], [26], [27]), Penot ([21], [22]) among others.In an attempt to explore in more detail relationships between various types of generalized directional derivatives we discovered some unexpected results which were not observed by the above mentioned authors. We are able to give simple conditions which characterize directionally Lipschitzian functions defined on a Baire metrizable locally convex topological vector space.

scholarly journals Generalised Hölderian functions

1989 ◽  
Vol 40 (1) ◽  
pp. 147-155
Author(s):  
S. De Sarkar ◽  
S. Panda
Keyword(s):  
Continuous Functions ◽  
Higher Order ◽  
Positive Order ◽  
New Class ◽  
Lipschitzian Functions ◽  
Relationship Of ◽  
The Relationship ◽  
Class Of Functions

The concept of kth Hölderian functions on an interval [a, b] which generalises the notion of Hölderian (Lipschitzian) functions of positive order on [a, b] is introduced. The relationship of such functions to functions of bounded kth variation and absolutely kth continuous functions is examined. Properties induced by higher order derivatives in this new class of functions are investigated.

On the qualitative approximation of Lipschitzian functions

2004 ◽  
Vol 56 (2) ◽  
pp. 289-307 ◽  
Author(s):  
Marı́a Alonso ◽  
Luis Rodrı́guez Marı́n
Keyword(s):  
Lipschitzian Functions
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