]>
2018
11
7
ISSN 2008-1898
69
Weakly invariant subspaces for multivalued linear operators on Banach spaces
Weakly invariant subspaces for multivalued linear operators on Banach spaces
en
en
Peter Saveliev generalized Lomonosov's invariant subspace theorem to the case of linear relations. In particular, he proved that if \(\mathcal S\) and \(\mathcal T\) are linear relations defined on a Banach space \(X\) and having finite dimensional multivalued parts and if \(\mathcal T\) right commutes with \(\mathcal S\), that is, \(\mathcal S \mathcal T \subset \mathcal T\mathcal S\), and if \(\mathcal S\) is compact then \(\mathcal T\) has a nontrivial weakly invariant subspace. However, the case of left commutativity remained open. In this paper, we develop some operator representation techniques for linear relations and use them to solve the left commutativity case mentioned above under the assumption that \(\mathcal S\mathcal T(0) = \mathcal S(0)\) and \(\mathcal T\mathcal S(0) = \mathcal T(0)\).
877
884
Gerald
Wanjala
Department of Mathematics and Statistics
Sultan Qaboos University
Sultanate of Oman
gwanjala@squ.edu.om;wanjalag@yahoo.com
Linear relations
weakly invariant subspaces
Article.1.pdf
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]
Sharpening and generalizations of Shafer-Fink and Wilker type inequalities: a new approach
Sharpening and generalizations of Shafer-Fink and Wilker type inequalities: a new approach
en
en
In this paper, we propose and prove some generalizations and sharpenings of certain inequalities
of Wilker's and Shafer-Fink's type. Application of the Wu-Debnath
theorem enabled us to prove some double sided inequalities.
885
893
Marija
Rašajski
School of Electrical Engineering
University of Belgrade
Serbia
marija.rasajski@etf.rs
Tatjana
Lutovac
School of Electrical Engineering
University of Belgrade
Serbia
tatjana.lutovac@etf.rs
Branko
Malešević
School of Electrical Engineering
University of Belgrade
Serbia
branko.malesevic@etf.rs
Sharpening
generalization
inequalities of Wilker's and Shafer-Fink's type
Article.2.pdf
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]
Superstability of Kannappan's and Van vleck's functional equations
Superstability of Kannappan's and Van vleck's functional equations
en
en
In this paper, we prove the superstability theorems of the
functional equations
\[\mu(y)f(x\sigma(y)z_0)\pm f(xyz_0) =2f(x)f(y), \;x,y\in S,\quad
\mu(y)f( \sigma(y)xz_0)\pm f(xyz_0) = 2f(x)f(y), \;x,y\in S,\]
where \(S\) is a semigroup, \(\sigma\) is an involutive morphism of \(S\),
and \(\mu:\) \(S\longrightarrow \mathbb{C}\) is a bounded multiplicative
function such that \(\mu(x\sigma(x))=1\) for all \(x \in S\), and
\(z_{0}\) is in the center of \(S\).
894
915
Belfakih
Keltouma
Faculty of Sciences, Department of Mathematics,
University Ibn Zohr
Morocco
Elqorachi
Elhoucien
Faculty of Sciences, Department of Mathematics,
University Ibn Zohr
Morocco
elqorachi@hotmail.com
Themistocles M.
Rassias
Department of Mathematics
National Technical University of Athens, Zofrafou Campus
Greece
Redouani
Ahmed
Faculty of Sciences, Department of Mathematics
University Ibn Zohr
Morocco
Hyers-Ulam stability
semigroup
d'Alembert's equation
automorpnism
multiplicative function
Article.3.pdf
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]
On the existence problem of solutions to a class of fuzzy mixed exponential vector variational inequalities
On the existence problem of solutions to a class of fuzzy mixed exponential vector variational inequalities
en
en
In this research article, we deal with a new kind of mixed
exponential fuzzy vector variational inequalities in ordered
Euclidean spaces. By using KKM-technique and Nadler's fixed point
theorem, we prove some existence theorems of solutions to mixed
exponential vector variational inequality problems in fuzzy
environment.
916
926
Shih-Sen
Chang
Center for General Education
China Medical University
Taiwan
S.
Salahuddin
Department of Mathematics
Jazan University
Kingdom of Saudi Arabia
Ching-Feng
Wen
Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization
Department of Medical Research
Kaohsiung Medical University
Kaohsiung Medical University Hospital
Taiwan
Taiwan
cfwen@kmu.edu.tw
Xiong Rui
Wang
Department of Mathematics
Yibin University
China
Mixed exponential vector variational inequality problems
fuzzy mappings
fuzzy upper and lower semicontinuous mappings
\(\alpha_g\)-relaxed exponentially \((\gamma,\eta)\)-monotone mapping
KKM-mappings
Nadler's fixed points theorem
ordered Euclidean spaces
Article.4.pdf
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P. Q. Khanh, N. H. Quan , Generic stability and essential components of generalized KKM points and applications, J. Optim. Theory Appl., 148 (2011), 488-504
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]
Projection algorithms with dynamic stepsize for constrained composite minimization
Projection algorithms with dynamic stepsize for constrained composite minimization
en
en
The problem of minimizing the sum of a large number of component
functions over the intersection of a finite family of closed convex
subsets of a Hilbert space is researched in the present paper. In
the case of the number of the component functions is huge, the
incremental projection methods are frequently used. Recently, we
have proposed a new incremental gradient projection algorithm for
this optimization problem. The new algorithm is parameterized by a
single nonnegative constant \(\mu\). And the algorithm is proved to
converge to an optimal solution if the dimensional of the Hilbert
space is finite the step size is diminishing (such as
\(\alpha_n=\mathcal{O}(1/n)\)). In this paper, the algorithm is
modified by employing the constant and the dynamic stepsize, and
the corresponding convergence properties are analyzed.
927
936
Yujing
Wu
Tianjin Vocational Institute
P. R. China
xiaomi20062008@163.com
Luoyi
Shi
Department of Mathematics
Tianjin Polytechnic University
P. R. China
shiluoyi@tjpu.edu.cn
Rudong
Chen
Department of Mathematics
Tianjin Polytechnic University
P. R. China
chenrd@tjpu.edu.cn
Composite minimization
projection algorithm
dynamic stepsize
Article.5.pdf
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]
On the oscillation for \(n\)th-order nonlinear neutral delay dynamic equations on time scales
On the oscillation for \(n\)th-order nonlinear neutral delay dynamic equations on time scales
en
en
In this paper, we investigate the solution's oscillation of \(n\)th-order nonlinear dynamic equation
\[[a_{n}(t)((a_{n-1}(t)(\cdots(a_{1}(t)(x(t)-p(t)x(\tau(t)))^{\Delta})^{\alpha_{1}})^{\Delta} \cdots)^{\Delta})^{\alpha_{n}}]^{\Delta}+f(t,x(\delta(t)))=0\]
on a time scale \(\mathbb{T}\) with \(n\geq 2\). We give some conditions for the oscillation of the above equation.
937
946
Yaru
Zhou
College of Mathematics and Information Science
Guangxi University
P. R. China
2416482188@qq.com
Zhanhe
Chen
College of Mathematics and Information Science
Guangxi University
P. R. China
czhhxl@gxu.edu.cn
Taixiang
Sun
Department of Mathematics
Guangxi College of Finance and Economics
P. R. China
stxhql@gxu.edu.cn
Oscillation
dynamic equation
time scale
Article.6.pdf
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[1]
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]