Convergence of operators

1985 ◽  
pp. 29-44
Author(s):  
Piotr Antosik ◽  
Charles Swartz
Keyword(s):  
Convergence Of Operators

Uniform convergence of operators onL ? and similar spaces

1985 ◽  
Vol 190 (2) ◽  
pp. 207-220 ◽  
Author(s):  
Heinrich P. Lotz
Keyword(s):  
Uniform Convergence ◽  
Convergence Of Operators

scholarly journals Convergence Theorems for Operators Sequences on Functionals of Discrete-Time Normal Martingales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jinshu Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Functional Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Convergence Of Operators

We aim to investigate the convergence of operators sequences acting on functionals of discrete-time normal martingales M. We first apply the 2D-Fock transform for operators from the testing functional space S(M) to the generalized functional space S⁎(M) and obtain a necessary and sufficient condition for such operators sequences to be strongly convergent. We then discuss the integration of these operator-valued functions. Finally, we apply the results obtained here and establish the existence and uniqueness of solution to quantum stochastic differential equations in terms of operators acting on functionals of discrete-time normal martingales M. And also we prove the continuity and continuous dependence on initial values of the solution.

scholarly journals Continuous dependence results for a class of evolution inclusions

1992 ◽  
Vol 35 (1) ◽  
pp. 139-158 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Continuous Dependence ◽  
Differential Inclusions ◽  
Solution Set ◽  
Evolution Inclusion ◽  
Evolution Inclusions ◽  
Upper Semicontinuous ◽  
Partial Differential Inclusions ◽  
General Existence ◽  
Convergence Of Operators ◽  
Continuous Dependence Results

In this paper we examine the dependence of the solutions of an evolution inclusion on a parameter λ We prove two dependence theorems. In the first the parameter appears only in the orientor field and we show that the solution set depends continuously on it for both the Vietoris and Hausdorff topologies. In the second the parameter appears also in the monotone operator. Using the notion of G-convergence of operators we prove that the solution set is upper semicontinuous with respect to the parameter. Both results make use of a general existence theorem which we also prove in this paper. Finally, we present two examples. One from control theory and the other from partial differential inclusions.

Generic power convergence of operators in banach spaces

1999 ◽  
Vol 20 (7-8) ◽  
pp. 629-650 ◽  
Author(s):  
Dan Butnariu ◽  
Simeon Reich ◽  
Alexander J. Zaslavski
Keyword(s):  
Banach Spaces ◽  
Convergence Of Operators

scholarly journals Approximation by Szász-Jakimovski-Leviatan-Type Operators via Aid of Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Present Article ◽  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Linear Operators ◽  
Approximation Properties ◽  
Appell Polynomials ◽  
Weighted Modulus Of Continuity ◽  
Dunkl Analogue ◽  
Weighted Modulus ◽  
Convergence Of Operators

The main purpose of the present article is to construct a newly Szász-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate the approximation properties of these operators, first we estimate the moments and obtain the basic results. Further, we study the approximation by the use of modulus of continuity in the spaces of the Lipschitz functions, Peetres K-functional, and weighted modulus of continuity. Moreover, we study A-statistical convergence of operators and approximation properties of the bivariate case.

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