scholarly journals Locally Defined Operators in the Space of Functions of Bounded Riesz-Variation

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
W. Aziz ◽  
J. A. Guerrero ◽  
K. Maldonado ◽  
N. Merentes
Keyword(s):  
Nemytskii Operator

We study the locally defined operator on the spaces of bounded Rieszp-variation functions and we prove that those operators are the Nemytskii operator.

scholarly journals On the Nemytskii Operator in the Space of Functions of Bounded (p, 2, α)-Variation with Respect to the Weight Function

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Wadie Aziz
Keyword(s):  
Weight Function ◽  
Bounded Variation ◽  
The Other ◽  
Affine Function ◽  
Nemytskii Operator ◽  
Other Hand ◽  
Generator Function ◽  
Uniformly Continuous

AbstractIn this paper, we consider the Nemytskii operator (Hf)(t) = h(t, f(t)), generated by a given function h. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded (p,2,α)-variation (with respect to a weight function α) into the space of functions of bounded (q,2,α)-variation (with respect to α) 1<q<p, then H is of the form (Hf)(t) = A(t)f(t)+B(t). On the other hand, if 1<p<q then H is constant. It generalize several earlier results of this type due to Matkowski-Merentes and Merentes. Also, we will prove that if a uniformly continuous Nemytskii operator maps a space of bounded variation with weight function in the sense of Merentes into another space of the same type, its generator function is an affine function.

On Stability of Continuous Extensions of Mappings with Respect to Nemytskii Operator

2020 ◽  
Vol 101 (3) ◽  
pp. 182-184
Author(s):  
A. V. Arutyunov ◽  
S. E. Zhukovskiy
Keyword(s):  
Nemytskii Operator

Nemytskii operator on $$(\phi ,2,\alpha )$$-bounded variation space in the sense of Riesz

2020 ◽  
Vol 11 (4) ◽  
pp. 2023-2043
Author(s):  
René E. Castillo ◽  
Edixon M. Rojas ◽  
Eduard Trousselot
Keyword(s):  
Bounded Variation ◽  
Nemytskii Operator

scholarly journals Some inequalities and superposition operator in the space of regulated functions

2019 ◽  
Vol 9 (1) ◽  
pp. 1278-1290 ◽  
Author(s):  
Leszek Olszowy ◽  
Tomasz Zając
Keyword(s):  
Hausdorff Measure ◽  
Necessary Conditions ◽  
Continuous Functions ◽  
Superposition Operator ◽  
Space Of Continuous Functions ◽  
Measures Of Noncompactness ◽  
Nemytskii Operator ◽  
Sufficient And Necessary Conditions ◽  
Regulated Functions

Abstract Some inequalities connected to measures of noncompactness in the space of regulated function R(J, E) were proved in the paper. The inequalities are analogous of well known estimations for Hausdorff measure and the space of continuous functions. Moreover two sufficient and necessary conditions that superposition operator (Nemytskii operator) can act from R(J, E) into R(J, E) are presented. Additionally, sufficient and necessary conditions that superposition operator Ff : R(J, E) → R(J, E) was compact are given.

scholarly journals The Nemytskii operator on bounded ö-variation in the mean spaces

2013 ◽  
Vol 32 (2) ◽  
pp. 119-142
Author(s):  
René Erlin Castillo ◽  
Nelson Merentes ◽  
Eduard Trousselot
Keyword(s):  
Nemytskii Operator ◽  
The Mean

scholarly journals Weak convergence under nonlinearities

2003 ◽  
Vol 75 (1) ◽  
pp. 9-19 ◽  
Author(s):  
DIEGO R. MOREIRA ◽  
EDUARDO V. O. TEIXEIRA
Keyword(s):  
Functional Equation ◽  
Weak Convergence ◽  
Resolvent Operator ◽  
Convergent Sequence ◽  
Regularity Result ◽  
Weak Continuity ◽  
Nonlinear Functional Equation ◽  
Nonlinear Functional ◽  
Nemytskii Operator ◽  
Sequential Continuity

In this paper, we prove that if a Nemytskii operator maps Lp(omega, E) into Lq(omega, F), for p, q greater than 1, E, F separable Banach spaces and F reflexive, then a sequence that converge weakly and a.e. is sent to a weakly convergent sequence. We give a counterexample proving that if q = 1 and p is greater than 1 we may not have weak sequential continuity of such operator. However, we prove that if p = q = 1, then a weakly convergent sequence that converges a.e. is mapped into a weakly convergent sequence by a Nemytskii operator. We show an application of the weak continuity of the Nemytskii operators by solving a nonlinear functional equation on W1,p(omega), providing the weak continuity of some kind of resolvent operator associated to it and getting a regularity result for such solution.

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