ORIGINAL_ARTICLE
Arens-irregularity of tensor product of Banach algebras
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.
https://ijnaa.semnan.ac.ir/article_110_b4abcb01c04089ee8011111f76b3eb00.pdf
2014-01-01
1
8
10.22075/ijnaa.2014.110
Arens products
Arens regularity
compact operators
approximable operators
nuclear operators
tensor norm
approximate identity
approximation property
T.
Yazdanpanah
1
Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran
LEAD_AUTHOR
R.
Gharibi
2
Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran
AUTHOR
ORIGINAL_ARTICLE
Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces
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.
https://ijnaa.semnan.ac.ir/article_111_3aee2736a32d307e34b4d8bc34fafb5a.pdf
2014-01-01
9
22
10.22075/ijnaa.2014.111
Infinitely differentiable functions
Function algebra
Lipschitz algebra
Maximal ideal space
Star-shaped set
Uniformly regular
D.
Alimohammadi
1
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
LEAD_AUTHOR
F.
Nezamabadi
2
Department of Mathematics, Faculty of Science, Arak University, P. O. Box: 38156-8-8349, Arak, Iran.
AUTHOR
ORIGINAL_ARTICLE
Ternary $(\sigma,\tau,\xi)$-derivations on Banach ternary algebras
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.
https://ijnaa.semnan.ac.ir/article_112_ecfffaca50a5c1a9f09e21fc58595127.pdf
2014-01-01
23
35
10.22075/ijnaa.2014.112
Banach ternary algebra
Banach ternary $A$-module
Ternary $(sigma,tau,xi)$-derivation
M.
Eshaghi Gordji
1
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
LEAD_AUTHOR
F.
Farrokhzad
2
Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
AUTHOR
S.A.R.
Hosseinioun
3
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA
AUTHOR
ORIGINAL_ARTICLE
Contractive maps in Mustafa-Sims metric spaces
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.
https://ijnaa.semnan.ac.ir/article_113_0b35677d1efa6cc2becda06023b6e04d.pdf
2014-01-01
36
53
10.22075/ijnaa.2014.113
metric space
globally strong Picard operator
functional anticipative contraction
Dhage and Mustafa-Sims metric
convergent and Cauchy sequence
strong triangle inequality
M.
Turinici
1
"A. Myller" Mathematical Seminar, "A. I. Cuza" University, 700506 Iasi, Romania
LEAD_AUTHOR
ORIGINAL_ARTICLE
Tripled partially ordered sets
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.
https://ijnaa.semnan.ac.ir/article_114_42e7a53b23613e649516a8991bc7f54e.pdf
2014-01-01
54
63
10.22075/ijnaa.2014.114
partially ordered set
upper bound
Lower bound
monotone function
M.
Eshaghi
1
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran
LEAD_AUTHOR
A.
Jabbari
2
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran
AUTHOR
S.
Mohseni
3
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
AUTHOR
ORIGINAL_ARTICLE
A fixed point result for a new class of set-valued contractions
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.
https://ijnaa.semnan.ac.ir/article_115_04704abdd8d440603dc84fa5e05cfff9.pdf
2014-01-01
64
70
10.22075/ijnaa.2014.115
Fixed point
Set-valued contraction
A.
Sadeghi Hafjejani
1
Department of Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran.
AUTHOR
A.
Amini Harandi
2
Department of Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
On a more accurate multiple Hilbert-type inequality
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.
https://ijnaa.semnan.ac.ir/article_116_ea3df0090bfbe87b3cfe918003fb4766.pdf
2014-01-01
71
79
10.22075/ijnaa.2014.116
Multiple Hilbert-Type Inequality
weight coefficient
Euler-Maclaurin’s Summation Formula
Q.
Huang
1
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
AUTHOR
B.
Yang
2
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
LEAD_AUTHOR
ORIGINAL_ARTICLE
A multidimensional discrete Hilbert-type inequality
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.
https://ijnaa.semnan.ac.ir/article_117_ad1285ddb601787b355b2ddbba08a66f.pdf
2014-01-01
80
88
10.22075/ijnaa.2014.117
Hilbert’s Inequality
weight coefficient
equivalent form
operator
norm
B.
Yang
1
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China.
LEAD_AUTHOR
ORIGINAL_ARTICLE
A companion of Ostrowski's inequality for functions of bounded variation and applications
A companion of Ostrowski's inequality for functions of bounded variation and applications are given.
https://ijnaa.semnan.ac.ir/article_118_8b6d57c3efcc79541d89acc0de017063.pdf
2014-01-01
89
97
10.22075/ijnaa.2014.118
Ostrowski’s Inequality
Trapezoid Rule
Midpoint Rule
S.S.
Dragomir
1
School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Some new extensions of Hardy`s inequality
In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequality in two and three dimensions
https://ijnaa.semnan.ac.ir/article_119_3350455c94f51970ab2121f655161633.pdf
2014-01-01
98
109
10.22075/ijnaa.2014.119
Hardy‘s inequality
Integral inequality
Riemann-Lioville integral
A.R.
Moazzen
1
Department of Mathematics, Velayat University, Iranshahr, Iran.
LEAD_AUTHOR
R.
Lashkaripour
2
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
AUTHOR