scholarly journals Covering numbers for bounded variation functions

2018 ◽  
Vol 468 (2) ◽  
pp. 1131-1143
Author(s):  
Prerona Dutta ◽  
Khai T. Nguyen
Keyword(s):  
Bounded Variation ◽  
Covering Numbers ◽  
Bounded Variation Functions

scholarly journals A note on integral modification of the Meyer-König and Zeller operators

2003 ◽  
Vol 2003 (31) ◽  
pp. 2003-2009 ◽  
Author(s):  
Vijay Gupta ◽  
Niraj Kumar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Present Note ◽  
Sharp Estimate ◽  
Functions Of Bounded Variation ◽  
Exact Bound ◽  
Bounded Variation Functions ◽  
Correct Estimate

Guo (1988) introduced the integral modification of Meyer-Kö nig and Zeller operatorsMˆnand studied the rate of convergence for functions of bounded variation. Gupta (1995) gave the sharp estimate for the operatorsMˆn. Zeng (1998) gave the exact bound and claimed to improve the results of Guo and Gupta, but there is a major mistake in the paper of Zeng. In the present note, we give the correct estimate for the rate of convergence on bounded variation functions.

DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750048 ◽  
Author(s):  
Y. S. LIANG
Keyword(s):  
Fractal Dimension ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
One Dimensional ◽  
Nondifferentiable Functions ◽  
Differentiable Functions ◽  
Closed Intervals ◽  
Bounded Variation Functions

The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.

On Bounded Variation Functions by General MKZD Operators

2006 ◽  
Vol 23 (8) ◽  
pp. 1457-1462 ◽  
Author(s):  
Vijay Gupta*
Keyword(s):  
Bounded Variation ◽  
Bounded Variation Functions

scholarly journals The Jordan decomposition of bounded variation functions valued in vector spaces

2017 ◽  
Vol 2 (4) ◽  
pp. 635-646
Author(s):  
Francisco J. Mendoza-Torres ◽  
◽  
Juan A. Escamilla-Reyna ◽  
Daniela Rodríguez-Tzompantzi
Keyword(s):  
Bounded Variation ◽  
Vector Spaces ◽  
Jordan Decomposition ◽  
Bounded Variation Functions

Uniformly Bounded Composition Operators on the Space of Bounded Variation Functions in the Sense of Waterman

2016 ◽  
Vol 13 (6) ◽  
pp. 4305-4320
Author(s):  
Wadie Aziz ◽  
Tomas Ereú ◽  
José A. Guerrero
Keyword(s):  
Bounded Variation ◽  
Composition Operators ◽  
Bounded Variation Functions ◽  
Uniformly Bounded

scholarly journals Global Components of Positive Bounded Variation Solutions of a One-Dimensional Indefinite Quasilinear Neumann Problem

2019 ◽  
Vol 19 (3) ◽  
pp. 437-473 ◽  
Author(s):  
Julian López-Gómez ◽  
Pierpaolo Omari
Keyword(s):  
Neumann Problem ◽  
Positive Solutions ◽  
Bounded Variation ◽  
Connected Components ◽  
One Dimensional ◽  
Linearized Problem ◽  
Bounded Variation Functions ◽  
The One ◽  
First Time ◽  
Prime 2

Abstract This paper investigates the topological structure of the set of the positive solutions of the one-dimensional quasilinear indefinite Neumann problem \begin{dcases}-\Bigg{(}\frac{u^{\prime}}{\sqrt{1+{u^{\prime}}^{2}}}\Bigg{)}^{% \prime}=\lambda a(x)f(u)\quad\text{in }(0,1),\\ u^{\prime}(0)=0,\quad u^{\prime}(1)=0,\end{dcases} where {\lambda\in\mathbb{R}} is a parameter, {a\in L^{\infty}(0,1)} changes sign, and {f\in C^{1}(\mathbb{R})} is positive in {(0,+\infty)} . The attention is focused on the case {f(0)=0} and {f^{\prime}(0)=1} , where we can prove, likely for the first time in the literature, a bifurcation result for this problem in the space of bounded variation functions. Namely, the existence of global connected components of the set of the positive solutions, emanating from the line of the trivial solutions at the two principal eigenvalues of the linearized problem around 0, is established. The solutions in these components are regular, as long as they are small, while they may develop jump singularities at the nodes of the weight function a, as they become larger, thus showing the possible coexistence along the same component of regular and singular solutions.

Sign in / Sign up

Export Citation Format

Share Document