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

The form of locally defined operators in waterman spaces

2021 ◽  
Vol 71 (6) ◽  
pp. 1529-1544
Author(s):  
Małgorzata Wróbel
Keyword(s):  
Banach Spaces ◽  
Bounded Variation ◽  
Composition Operators ◽  
Representation Formula ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
Spaces Of Continuous Functions ◽  
Local Operators ◽  
Uniformly Bounded

Abstract A representation formula for locally defined operators acting between Banach spaces of continuous functions of bounded variation in the Waterman sense is presented. Moreover, the Nemytskij composition operators will be investigated and some consequences for locally bounded as well as uniformly bounded local operators will be given.

Uniformly continuous composition operators in the space of bounded -variation functions

2010 ◽  
Vol 72 (6) ◽  
pp. 3119-3123 ◽  
Author(s):  
J.A. Guerrero ◽  
H. Leiva ◽  
J. Matkowski ◽  
N. Merentes
Keyword(s):  
Bounded Variation ◽  
Composition Operators ◽  
Bounded Variation Functions ◽  
Uniformly Continuous

scholarly journals Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

2015 ◽  
Vol 14 (4) ◽  
pp. 41-51
Author(s):  
José Atilio Guerrero ◽  
◽  
Janusz Matkowski ◽  
Nelson Merentes ◽  
Małgorzata Wróbel ◽  
...  
Keyword(s):  
Bounded Variation ◽  
Composition Operators ◽  
Functions Of Bounded Variation ◽  
Bounded Set ◽  
Uniformly Bounded

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.

scholarly journals UNIFORMLY BOUNDED COMPOSITION OPERATORS ON A BANACH SPACE OF BOUNDED WIENER-YOUNG VARIATION FUNCTIONS

2013 ◽  
Vol 50 (2) ◽  
pp. 675-685 ◽  
Author(s):  
Dorota Glazowska ◽  
Jose Atilio Guerrero ◽  
Janusz Matkowski ◽  
Nelson Merentes
Keyword(s):  
Banach Space ◽  
Composition Operators ◽  
Uniformly Bounded

UNIFORMLY BOUNDED COMPOSITION OPERATORS

2015 ◽  
Vol 92 (3) ◽  
pp. 463-469
Author(s):  
DOROTA GŁAZOWSKA ◽  
JANUSZ MATKOWSKI
Keyword(s):  
Weight Function ◽  
Composition Operators ◽  
Function Variable ◽  
Nemytskij Operator ◽  
Uniformly Bounded

We prove that if a uniformly bounded (or equidistantly uniformly bounded) Nemytskij operator maps the space of functions of bounded ${\it\varphi}$-variation with weight function in the sense of Riesz into another space of that type (with the same weight function) and its generator is continuous with respect to the second variable, then this generator is affine in the function variable (traditionally, in the second variable).

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.

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