A new sequence space and norm of certain matrix operators on this space
Hadi
Roopaei
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
author
Davoud
Foroutannia
Department of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran.
author
text
article
2016
eng
In the present paper, we introduce the sequence space \[{l_p}(E,\Delta) = \left\{ x = (x_n)_{n = 1}^\infty : \sum_{n = 1}^\infty \left| \sum_{j \in {E_n}} x_j - \sum_{j \in E_{n + 1}} x_j\right| ^p < \infty \right\},\] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $p\ge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding the norm of certain matrix operators from $l_p$ into $ l_p(E,\Delta)$, and apply our results to Copson and Hilbert matrices.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
03
v.
1
no.
2016
1
12
https://scma.maragheh.ac.ir/article_18569_d37578addf12775560a0dd1348a14dea.pdf
The approximate solutions of Fredholm integral equations on Cantor sets within local fractional operators
Hassan
Kamil Jassim
Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq.
author
text
article
2016
eng
In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools for solving local fractional integral equations.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
03
v.
1
no.
2016
13
20
https://scma.maragheh.ac.ir/article_17845_a652d4a96c5d40bec32124ba5a31274e.pdf
Some properties of fuzzy real numbers
Bayaz
Daraby
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
author
Javad
Jafari
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
author
text
article
2016
eng
In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers.
In this study, we try to prove Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
03
v.
1
no.
2016
21
27
https://scma.maragheh.ac.ir/article_18685_8eb1db4d00d23665dcf2e7857784a827.pdf
Some study on the growth properties of entire functions represented by vector valued Dirichlet series in the light of relative Ritt orders
Sanjib
Datta
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-\ 741235, West Bengal, India.
author
Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
author
Pranab
Das
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
author
text
article
2016
eng
For entire functions, the notions of their growth indicators such as Ritt order are classical in complex analysis. But the concepts of relative Ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $\exp \exp z$ are not at all known to the researchers of this area. Therefore the studies of the growths of entire functions in the light of their relative Ritt order are the prime concern of this paper. Actually in this paper we establish some newly developed results related to the growth rates of entire functions on the basis of their relative Ritt order (respectively, relative Ritt lower order).
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
03
v.
1
no.
2016
29
35
https://scma.maragheh.ac.ir/article_18094_663f26d0249c7fa7dd6e83e21ad32d04.pdf
Numerical solution of a class of nonlinear two-dimensional integral equations using Bernoulli polynomials
Sohrab
Bazm
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
author
text
article
2016
eng
In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficiency and accuracy of the method.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
03
v.
1
no.
2016
37
51
https://scma.maragheh.ac.ir/article_15994_6d676e68a2b7a882c1334cdc50d1acf4.pdf
On strongly Jordan zero-product preserving maps
Ali Reza
Khoddami
Department of Pure Mathematics, University of Shahrood, P. O. Box 3619995161-316, Shahrood, Iran.
author
text
article
2016
eng
In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct product and the composition of two strongly Jordan zero-product preserving maps are again strongly Jordan zero-product preserving maps. But this fact is not the case for tensor product of them in general. Finally, we prove that every $*-$preserving linear map from a normed $*-$algebra into a $C^*-$algebra that strongly preserves Jordan zero-products is necessarily continuous.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
03
v.
1
no.
2016
53
61
https://scma.maragheh.ac.ir/article_18096_d23368a43afbd4357de9825202e142e0.pdf
Parabolic starlike mappings of the unit ball $B^n$
Samira
Rahrovi
Department of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551-761167, Bonab, Iran.
author
text
article
2016
eng
Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^n\subseteq\mathbb{C}^n$ given by $$\Phi_{n,\gamma}(f)(z)=\left(f(z_1),(f'(z_1))^\gamma\hat{z}\right),$$ where $\gamma\in[0,1/2]$, $z=(z_1,\hat{z})\in B^n$ and $$\Psi_{n,\beta}(f)(z)=\left(f(z_1),(\frac{f(z_1)}{z_1})^\beta\hat{z}\right),$$ in which $\beta\in[0,1]$, $f(z_1)\neq 0$ and $z=(z_1,\hat{z})\in B^n$. In the case $\gamma=1/2$, the function $\Phi_{n,\gamma}(f)$ reduces to the well known Roper-Suffridge extension operator. By using different methods, we prove that if $f$ is parabolic starlike mapping on $U$ then $\Phi_{n,\gamma}(f)$ and $\Psi_{n,\beta}(f)$ are parabolic starlike mappings on $B^n$.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
03
v.
1
no.
2016
63
70
https://scma.maragheh.ac.ir/article_17820_b9493019b43e586b7325e86fcd33c0a4.pdf