Arens-irregularity of tensor product of Banach algebras
T.
Yazdanpanah
Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran
author
R.
Gharibi
Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran
author
text
article
2014
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
1
8
https://ijnaa.semnan.ac.ir/article_110_b4abcb01c04089ee8011111f76b3eb00.pdf
dx.doi.org/10.22075/ijnaa.2014.110
Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces
D.
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
author
F.
Nezamabadi
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
author
text
article
2014
eng
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 $m, n \in\mathbb{N} \cup\{0\}$ and $\alpha\in (0, 1]$. Let $d =\lim \sup(\frac{n!}{M_n})^{\frac{1}{n}}$ and $X_d =\{z \in\mathbb{C} : dist(z,X)\leq d\}$. 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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
9
22
https://ijnaa.semnan.ac.ir/article_111_3aee2736a32d307e34b4d8bc34fafb5a.pdf
dx.doi.org/10.22075/ijnaa.2014.111
Ternary $(\sigma,\tau,\xi)$-derivations on Banach ternary algebras
M.
Eshaghi Gordji
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
author
F.
Farrokhzad
Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
author
S.A.R.
Hosseinioun
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA
author
text
article
2014
eng
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$$D([xyz]_A) = [D(x)\tau(y)\xi(z)]_X + [\sigma(x)D(y)\xi(z)]_X + [\sigma(x)\tau(y)D(z)]_X$$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$$f(\frac{x + y + z}{4}) + f(\frac{3x - y - 4z}{4}) + f(\frac{4x + 3z}{4}) = 2f(x).$$Moreover, we prove the generalized Ulam-Hyers stability of ternary $(\sigma,\tau,\xi)$-derivations on Banach ternary algebras.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
23
35
https://ijnaa.semnan.ac.ir/article_112_ecfffaca50a5c1a9f09e21fc58595127.pdf
dx.doi.org/10.22075/ijnaa.2014.112
Contractive maps in Mustafa-Sims metric spaces
M.
Turinici
"A. Myller" Mathematical Seminar, "A. I. Cuza" University, 700506 Iasi, Romania
author
text
article
2014
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
36
53
https://ijnaa.semnan.ac.ir/article_113_0b35677d1efa6cc2becda06023b6e04d.pdf
dx.doi.org/10.22075/ijnaa.2014.113
Tripled partially ordered sets
M.
Eshaghi
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran
author
A.
Jabbari
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran
author
S.
Mohseni
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
author
text
article
2014
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
54
63
https://ijnaa.semnan.ac.ir/article_114_42e7a53b23613e649516a8991bc7f54e.pdf
dx.doi.org/10.22075/ijnaa.2014.114
A fixed point result for a new class of set-valued contractions
A.
Sadeghi Hafjejani
Department of Mathematics, University of Shahrekord,
Shahrekord, 88186-34141, Iran.
author
A.
Amini Harandi
Department of Mathematics, University of Shahrekord,
Shahrekord, 88186-34141, Iran.
author
text
article
2014
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
64
70
https://ijnaa.semnan.ac.ir/article_115_04704abdd8d440603dc84fa5e05cfff9.pdf
dx.doi.org/10.22075/ijnaa.2014.115
On a more accurate multiple Hilbert-type inequality
Q.
Huang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
author
B.
Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
author
text
article
2014
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
71
79
https://ijnaa.semnan.ac.ir/article_116_ea3df0090bfbe87b3cfe918003fb4766.pdf
dx.doi.org/10.22075/ijnaa.2014.116
A multidimensional discrete Hilbert-type inequality
B.
Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China.
author
text
article
2014
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
80
88
https://ijnaa.semnan.ac.ir/article_117_ad1285ddb601787b355b2ddbba08a66f.pdf
dx.doi.org/10.22075/ijnaa.2014.117
A companion of Ostrowski's inequality for functions of bounded variation and applications
S.S.
Dragomir
School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050,
South Africa.
author
text
article
2014
eng
A companion of Ostrowski's inequality for functions of bounded variation and applications are given.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
89
97
https://ijnaa.semnan.ac.ir/article_118_8b6d57c3efcc79541d89acc0de017063.pdf
dx.doi.org/10.22075/ijnaa.2014.118
Some new extensions of Hardy`s inequality
A.R.
Moazzen
Department of Mathematics, Velayat University, Iranshahr, Iran.
author
R.
Lashkaripour
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
author
text
article
2014
eng
In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequality in two and three dimensions
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
5
v.
1 (Special Issue)
no.
2014
98
109
https://ijnaa.semnan.ac.ir/article_119_3350455c94f51970ab2121f655161633.pdf
dx.doi.org/10.22075/ijnaa.2014.119