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 8 110 10.22075/ijnaa.2014.110 EN T. Yazdanpanah Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran R. Gharibi Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran Journal Article 2014 02 17 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.
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 22 111 10.22075/ijnaa.2014.111 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. Journal Article 2014 02 17 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.
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 35 112 10.22075/ijnaa.2014.112 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 Journal Article 2014 02 19 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.
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 53 113 10.22075/ijnaa.2014.113 EN M. Turinici &quot;A. Myller&quot; Mathematical Seminar, &quot;A. I. Cuza&quot; University, 700506 Iasi, Romania Journal Article 2014 02 19 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.
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 5 1 (Special Issue) 2014 01 01 Tripled partially ordered sets 54 63 114 10.22075/ijnaa.2014.114 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. Journal Article 2014 02 19 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.
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 70 115 10.22075/ijnaa.2014.115 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. Journal Article 2014 02 20 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.
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 79 116 10.22075/ijnaa.2014.116 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 Journal Article 2014 02 20 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.
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 88 117 10.22075/ijnaa.2014.117 EN B. Yang Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China. Journal Article 2014 02 20 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.
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 97 118 10.22075/ijnaa.2014.118 EN S.S. Dragomir School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa. Journal Article 2014 02 20 A companion of Ostrowski's inequality for functions of bounded variation and applications are given.
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 98 109 119 10.22075/ijnaa.2014.119 EN A.R. Moazzen Department of Mathematics, Velayat University, Iranshahr, Iran. R. Lashkaripour Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran. Journal Article 2014 02 20 In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequality in two and three dimensions