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