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 &quot;A. Myller&quot; Mathematical Seminar, &quot;A. I. Cuza&quot; 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