Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
Arens-irregularity of tensor product of Banach algebras
1
8
EN
T.
Yazdanpanah
Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran
R.
Gharibi
Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran
10.22075/ijnaa.2014.110
We introduce Banach algebras arising from tensor norms. By these Banach algebras, we make Arens regular Banach algebras such that $alpha$ the tensor product becomes irregular, where $alpha$ is tensor norm. We illustrate injective tensor product, does not preserve bounded approximate identity and it is not algebra norm.
Arens products,Arens regularity,compact operators,approximable operators,nuclear operators,tensor norm,approximate identity,approximation property
https://ijnaa.semnan.ac.ir/article_110.html
https://ijnaa.semnan.ac.ir/article_110_b4abcb01c04089ee8011111f76b3eb00.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces
9
22
EN
D.
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
F.
Nezamabadi
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
10.22075/ijnaa.2014.111
We study an interesting class of Banach function algebras of infinitely differentiable functions on perfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, called Lipschitz algebras of infinitely differentiable functions and denoted by $Lip(X,M, alpha)$, where $X$ is a perfect, compact plane set, $M ={M_n}_{n=0}^infty$ is a sequence of positive numbers such that $M_0 = 1$ and $frac{(m+n)!}{M_{m+n}}leq(frac{m!}{M_m})(frac{n!}{M_n})$, for $m, n inmathbb{N} cup{0}$ and $alphain (0, 1]$. Let $d =lim sup(frac{n!}{M_n})^{frac{1}{n}}$ and $X_d ={z inmathbb{C} : dist(z,X)leq d}$. Let $Lip_{P,d}(X,M, alpha)$ [$Lip_{R,d}(X,M alpha)$] be the subalgebra of all $f in Lip(X,M,alpha)$ that can be approximated by the restriction to $X_d$ of polynomials [rational functions with poles $X_d$]. We show that the maximal ideal space of $Lip_{P,d}(X,M, alpha)$ is $widehat{X_d}$, the polynomially convex hull of $X_d$, and the maximal ideal space of $Lip_{R,d}(X,M alpha)$ is $X_d$, for certain compact plane sets. Using some formulae from combinatorial analysis, we find the maximal ideal space of certain subalgebras of Lipschitz algebras of infinitely differentiable functions.
Infinitely differentiable functions,Function algebra,Lipschitz algebra,Maximal ideal space,Star-shaped set,Uniformly regular
https://ijnaa.semnan.ac.ir/article_111.html
https://ijnaa.semnan.ac.ir/article_111_3aee2736a32d307e34b4d8bc34fafb5a.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
Ternary $(sigma,tau,xi)$-derivations on Banach ternary algebras
23
35
EN
M.
Eshaghi Gordji
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
F.
Farrokhzad
Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
S.A.R.
Hosseinioun
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA
10.22075/ijnaa.2014.112
Let $A$ be a Banach ternary algebra over a scalar field $mathbb{R}$ or $mathbb{C}$ and $X$ be a Banach ternary $A$-module. Let $sigma, tau$ and $xi$ be linear mappings on $A$, a linear mapping $D : (A,[ ]_A) to (X, [ ]_X)$ is called a ternary $(sigma,tau,xi)$-derivation, if<br />$$D([xyz]_A) = [D(x)tau(y)xi(z)]_X + [sigma(x)D(y)xi(z)]_X + [sigma(x)tau(y)D(z)]_X$$<br />for all $x,y, z in A$. In this paper, we investigate ternary $(sigma,tau,xi)$-derivation on Banach ternary algebras, associated with the following functional equation<br />$$f(frac{x + y + z}{4}) + f(frac{3x - y - 4z}{4}) + f(frac{4x + 3z}{4}) = 2f(x).$$<br />Moreover, we prove the generalized Ulam-Hyers stability of ternary $(sigma,tau,xi)$-derivations on Banach ternary algebras.
Banach ternary algebra,Banach ternary $A$-module,Ternary $(sigma,tau,xi)$-derivation
https://ijnaa.semnan.ac.ir/article_112.html
https://ijnaa.semnan.ac.ir/article_112_ecfffaca50a5c1a9f09e21fc58595127.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
Contractive maps in Mustafa-Sims metric spaces
36
53
EN
M.
Turinici
"A. Myller" Mathematical Seminar, "A. I. Cuza" University, 700506 Iasi, Romania
10.22075/ijnaa.2014.113
The fixed point results in Mustafa-Sims metrical structures obtained by Karapinar and Agarwal [Fixed Point Th. Appl., 2013, 2013:154] is deductible from a corresponding one stated in terms of anticipative contractions over the associated (standard) metric space.
metric space,globally strong Picard operator,functional anticipative contraction,Dhage and Mustafa-Sims metric,convergent and Cauchy sequence,strong triangle inequality
https://ijnaa.semnan.ac.ir/article_113.html
https://ijnaa.semnan.ac.ir/article_113_0b35677d1efa6cc2becda06023b6e04d.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
Tripled partially ordered sets
54
63
EN
M.
Eshaghi
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran
A.
Jabbari
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran
S.
Mohseni
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
10.22075/ijnaa.2014.114
In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partially ordered sets. Some basic properties on these new defined sets are studied and some examples for clarifying are given.
partially ordered set,upper bound,Lower bound,monotone function
https://ijnaa.semnan.ac.ir/article_114.html
https://ijnaa.semnan.ac.ir/article_114_42e7a53b23613e649516a8991bc7f54e.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
A fixed point result for a new class of set-valued contractions
64
70
EN
A.
Sadeghi Hafjejani
Department of Mathematics, University of Shahrekord,
Shahrekord, 88186-34141, Iran.
A.
Amini Harandi
Department of Mathematics, University of Shahrekord,
Shahrekord, 88186-34141, Iran.
10.22075/ijnaa.2014.115
In this paper, we introduce a new class of set-valued contractions and obtain a fixed point theorem for such mappings in complete metric spaces. Our main result generalizes and improves many well-known fixed point theorems in the literature.
Fixed point,Set-valued contraction
https://ijnaa.semnan.ac.ir/article_115.html
https://ijnaa.semnan.ac.ir/article_115_04704abdd8d440603dc84fa5e05cfff9.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
On a more accurate multiple Hilbert-type inequality
71
79
EN
Q.
Huang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
B.
Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
10.22075/ijnaa.2014.116
By using Euler-Maclaurin's summation formula and the way of real analysis, a more accurate multiple Hilbert-type inequality and the equivalent form are given. We also prove that the same constant factor in the equivalent inequalities is the best possible.
Multiple Hilbert-Type Inequality,weight coefficient,Euler-Maclaurin’s Summation Formula
https://ijnaa.semnan.ac.ir/article_116.html
https://ijnaa.semnan.ac.ir/article_116_ea3df0090bfbe87b3cfe918003fb4766.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
A multidimensional discrete Hilbert-type inequality
80
88
EN
B.
Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China.
10.22075/ijnaa.2014.117
In this paper, by using the way of weight coefficients and technique of real analysis, a multidimensional discrete Hilbert-type inequality with the best possible constant factor is given. The equivalent form, the operator expression with the norm are considered.
Hilbert’s Inequality,weight coefficient,equivalent form,operator,norm
https://ijnaa.semnan.ac.ir/article_117.html
https://ijnaa.semnan.ac.ir/article_117_ad1285ddb601787b355b2ddbba08a66f.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
A companion of Ostrowski's inequality for functions of bounded variation and applications
89
97
EN
S.S.
Dragomir
School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050,
South Africa.
10.22075/ijnaa.2014.118
A companion of Ostrowski's inequality for functions of bounded variation and applications are given.
Ostrowski’s Inequality,Trapezoid Rule,Midpoint Rule
https://ijnaa.semnan.ac.ir/article_118.html
https://ijnaa.semnan.ac.ir/article_118_8b6d57c3efcc79541d89acc0de017063.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
5
1 (Special Issue)
2014
01
01
Some new extensions of Hardy`s inequality
98
109
EN
A.R.
Moazzen
Department of Mathematics, Velayat University, Iranshahr, Iran.
R.
Lashkaripour
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
10.22075/ijnaa.2014.119
In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequality in two and three dimensions
Hardy‘s inequality,Integral inequality,Riemann-Lioville integral
https://ijnaa.semnan.ac.ir/article_119.html
https://ijnaa.semnan.ac.ir/article_119_3350455c94f51970ab2121f655161633.pdf