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2. Convergence estimate for second order Cauchy problems with a small parameter

Creator:
Najman, Branko
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math, second order initial value problem, and Hilbert space
Language:
English
Description:
We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter $\varepsilon .$ The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Some equivalent metrics for bounded normal operators

Creator:
Jabbarzadeh, Mohammad Reza and Hajipouri, Rana
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hilbert space, normal operator, equivalent metrics, and composition operator
Language:
English
Description:
Some stronger and equivalent metrics are defined on M, the set of all bounded normal operators on a Hilbert space H and then some topological properties of M are investigated.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Strong convergence theorems of $k$-strict pseudo-contractions in Hilbert spaces

Creator:
Qin, Xiaolong, Kang, Shin Min, and Shang, Meijuan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hilbert space, nonexpansive mapping, strict pseudo-contraction, iterative algorithm, and fixed point
Language:
English
Description:
Let $K$ be a nonempty closed convex subset of a real Hilbert space $H$ such that $K\pm K\subset K$, $T\: K\rightarrow H$ a $k$-strict pseudo-contraction for some $0\leq k<1$ such that $F(T)=\{x\in K\: x=Tx\}\neq \emptyset $. Consider the following iterative algorithm given by $$ \forall x_1\in K,\quad x_{n+1}=\alpha _n\gamma f(x_n)+\beta _nx_n+((1-\beta _n)I-\alpha _n A)P_KSx_n,\quad n\geq 1, $$ where $S\: K\rightarrow H$ is defined by $Sx=kx+(1-k)Tx$, $P_K$ is the metric projection of $H$ onto $K$, $A$ is a strongly positive linear bounded self-adjoint operator, $f$ is a contraction. It is proved that the sequence $\{x_n\}$ generated by the above iterative algorithm converges strongly to a fixed point of $T$, which solves a variational inequality related to the linear operator $A$. Our results improve and extend the results announced by many others.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public