scholarly journals On the Mikusiński-Antosik diagonal theorem and the equivalence of two types of convergence in Köthe spaces

2017 ◽  
Vol 101 (115) ◽  
pp. 151-160
Author(s):  
Andrzej Kamiński ◽  
Sławomir Sorek
Keyword(s):  
Weak Convergence ◽  
Simple Proof ◽  
Extended Form ◽  
Strong And Weak Convergence ◽  
Köthe Spaces ◽  
Convergence Of Sequences

We present a simple proof of the Mikusi?ski-Antosik diagonal theorem and apply this result to prove, in an extended form, the theorem on the equivalence of the strong and weak boundedness of sets and, consequently, of the strong and weak convergence of sequences in Kothe spaces.

1.—Perturbation Theory for Sobolev Spaces

1975 ◽  
Vol 73 ◽  
pp. 5-49 ◽  
Author(s):  
Friedrich Stummel
Keyword(s):  
Perturbation Theory ◽  
Weak Convergence ◽  
Sobolev Spaces ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Boundary Integrals ◽  
Strong And Weak Convergence ◽  
Discrete Compactness ◽  
Convergence Of Sequences ◽  
Basic Concepts

SynopsisThis paper studies Sobolev spaces under perturbation of domains of definition. It establishes the basic concepts, methods and results for the convergence of sequences of sets in ℝn, the strong and weak convergence of sequences of Sobolev spaces, the discrete compactness of natural embeddings and the continuous convergence of continuous linear functionals, boundary integrals and trace operators for sequences of Sobolev spaces.

scholarly journals Strong and Weak Convergence Theorems for Equilibrium Problems and Weak Relatively Uniformly Nonexpansive Multivalued Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Zi-Ming Wang
Keyword(s):  
Weak Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Common Element ◽  
Multivalued Mappings ◽  
Point Problem ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
The Common

Equilibrium problem and fixed point problem are considered. A general iterative algorithm is introduced for finding a common element of the set of solutions to the equilibrium problem and the common set of fixed points of two weak relatively uniformly nonexpansive multivalued mappings. Furthermore, strong and weak convergence results for the common element in the two sets mentioned above are established in some Banach space.

Weak convergence of an iterated renewal process

1981 ◽  
Vol 18 (01) ◽  
pp. 291-296
Author(s):  
Pranab Kumar Sen
Keyword(s):  
Weak Convergence ◽  
Asymptotic Normality ◽  
Invariance Principle ◽  
Simple Proof ◽  
Renewal Process ◽  
Weak Invariance Principle ◽  
Weak Invariance

Asymptotic normality and the weak invariance principle are studied for an iterated renewal process of order A martingale decomposition is used in this context to provide a simple proof.

scholarly journals Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
Somyot Plubtieng ◽  
Wanna Sriprad
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Convergence Rate ◽  
Minimization Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convex Minimization Problem ◽  
Mann Iteration ◽  
Strong And Weak Convergence

We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extend and improve the corresponding result of Ibaraki and Takahashi (2007), and Kim and Xu (2005).

Weak convergence of an iterated renewal process

1981 ◽  
Vol 18 (1) ◽  
pp. 291-296 ◽  
Author(s):  
Pranab Kumar Sen
Keyword(s):  
Weak Convergence ◽  
Asymptotic Normality ◽  
Invariance Principle ◽  
Simple Proof ◽  
Renewal Process ◽  
Weak Invariance Principle ◽  
Weak Invariance

Asymptotic normality and the weak invariance principle are studied for an iterated renewal process of order A martingale decomposition is used in this context to provide a simple proof.

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