2022-05-28T17:19:10Z
https://ijnaa.semnan.ac.ir/?_action=export&rf=summon&issue=21
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
Arens-irregularity of tensor product of Banach algebras
T.
Yazdanpanah
R.
Gharibi
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
2014
01
01
1
8
https://ijnaa.semnan.ac.ir/article_110_b4abcb01c04089ee8011111f76b3eb00.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces
D.
Alimohammadi
F.
Nezamabadi
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.
Infinitely differentiable functions
Function algebra
Lipschitz algebra
Maximal ideal space
Star-shaped set
Uniformly regular
2014
01
01
9
22
https://ijnaa.semnan.ac.ir/article_111_3aee2736a32d307e34b4d8bc34fafb5a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
Ternary $(sigma,tau,xi)$-derivations on Banach ternary algebras
M.
Eshaghi Gordji
F.
Farrokhzad
S.A.R.
Hosseinioun
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.
Banach ternary algebra
Banach ternary $A$-module
Ternary $(sigma,tau,xi)$-derivation
2014
01
01
23
35
https://ijnaa.semnan.ac.ir/article_112_ecfffaca50a5c1a9f09e21fc58595127.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
Contractive maps in Mustafa-Sims metric spaces
M.
Turinici
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
2014
01
01
36
53
https://ijnaa.semnan.ac.ir/article_113_0b35677d1efa6cc2becda06023b6e04d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
Tripled partially ordered sets
M.
Eshaghi
A.
Jabbari
S.
Mohseni
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
2014
01
01
54
63
https://ijnaa.semnan.ac.ir/article_114_42e7a53b23613e649516a8991bc7f54e.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
A fixed point result for a new class of set-valued contractions
A.
Sadeghi Hafjejani
A.
Amini Harandi
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
2014
01
01
64
70
https://ijnaa.semnan.ac.ir/article_115_04704abdd8d440603dc84fa5e05cfff9.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
On a more accurate multiple Hilbert-type inequality
Q.
Huang
B.
Yang
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
2014
01
01
71
79
https://ijnaa.semnan.ac.ir/article_116_ea3df0090bfbe87b3cfe918003fb4766.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
A multidimensional discrete Hilbert-type inequality
B.
Yang
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
2014
01
01
80
88
https://ijnaa.semnan.ac.ir/article_117_ad1285ddb601787b355b2ddbba08a66f.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
A companion of Ostrowski's inequality for functions of bounded variation and applications
S.S.
Dragomir
A companion of Ostrowski's inequality for functions of bounded variation and applications are given.
Ostrowski’s Inequality
Trapezoid Rule
Midpoint Rule
2014
01
01
89
97
https://ijnaa.semnan.ac.ir/article_118_8b6d57c3efcc79541d89acc0de017063.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2014
5
1 (Special Issue)
Some new extensions of Hardy`s inequality
A.R.
Moazzen
R.
Lashkaripour
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
2014
01
01
98
109
https://ijnaa.semnan.ac.ir/article_119_3350455c94f51970ab2121f655161633.pdf