ORIGINAL_ARTICLE
A new sequence space and norm of certain matrix operators on this space
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.
https://scma.maragheh.ac.ir/article_18569_d37578addf12775560a0dd1348a14dea.pdf
2016-02-01
1
12
Difference sequence space
Matrix domains
norm
Copson matrix
Hilbert matrix
Hadi
Roopaei
h.roopaei@gmail.com
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
AUTHOR
Davoud
Foroutannia
foroutan@vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
LEAD_AUTHOR
[1] B. Altay and F. Basar, The ne spectrum and the matrix domain of the dierence operator Δ on the sequence space lp, (0 < p < 1), Commun. Math. Anal., 2(2) (2007) 1-11.
1
[2] F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, Istanbul, 2012.
2
[3] F. Basar and B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, Ukr. Math. J., 55(1) (2003) 136-147.
3
[4] F. Basar, B. Altay, and M. Mursaleen, Some generalizations of the space bvp of p-bounded variation sequences, Nonlinear Anal., 68(2) (2008) 273-287.
4
[5] D. Foroutannia, On the block sequence space lp(E) and related matrix transfor- mations, Turk. J. Math., 39 (2015) 830-841.
5
[6] D. Foroutannia, Upper bound and lower bound for matrix opwrators on weighted sequence spaces, Doctoral dissertation, Zahedan, 2007.
6
[7] G.H. Hardy, J.E. Littlewood, and G. Polya, Inequalities, 2nd edition, Cambridge University press, Cambridge, 2001.
7
[8] G.J.O. Jameson and R. Lashkaripour, Norms of certain operators on weighted lp spaces and Lorentz sequence spaces, J. Inequal. Pure Appl. Math., 3(1) (2002) Article 6.
8
[9] H. Kizmaz, On certain sequence spaces I, Canad. Math. Bull., 25(2) (1981) 169-176.
9
[10] R. Lashkaripour and J. Fathi, Norms of matrix operators on bvp, J. Math. Inequal., 6(4) (2012) 589-592.
10
[11] M. Mursaleen and A.K. Noman, On some new dierence sequence spaces of non-absolute type, Math. Comput. Modelling, 52 (2010) 603-617.
11
[12] H. Roopaei and D. Foroutannia, The norm of certain matrix operators on the new dierence sequence spaces, preprint.
12
ORIGINAL_ARTICLE
The approximate solutions of Fredholm integral equations on Cantor sets within local fractional operators
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.
https://scma.maragheh.ac.ir/article_17845_a652d4a96c5d40bec32124ba5a31274e.pdf
2016-02-01
13
20
Fredholm integral equation
Local fractional Adomian decomposition method
Local fractional variational iteration method
Hassan
Kamil Jassim
hassan.kamil28@yahoo.com
1
Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq.
LEAD_AUTHOR
[1] H.K. Jassim, C. Unlu, S.P. Moshokoa, and C.M. Khalique, Local Fractional Laplace Variational Iteration Method for Solving Diusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015 Article ID 309870 (2015) 1-9.
1
[2] S.S. Ray and P.K. Sahu, Numerical Methods for Solving Fredholm Integral Equations of Second Kind, Abstract and Applied Analysis, 2013 Article ID 42916 (2013)1-17.
2
[3] C.T. Shieh and V.A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl., 347 (2008) 266-272.
3
[4] W.H. Su, D. Baleanu, X.J. Yang, and H. Jafari, Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method, Fixed Point Theory and Applications, 2013 Article 89 (2013) 1-7.
4
[5] A.M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications, Springer, New York, NY, USA, 2011.
5
[6] S.P. Yan, H. Jafari, and H.K. Jassim, Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014 Article ID 161580 (2014) 1-7.
6
[7] Y.J. Yang, D. Baleanu, and X.J. Yang, A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis, 2013 Article ID 202650 (2013) 1-6.
7
[8] Y.J. Yang, S.Q. Wang, and H.K. Jassim, Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014 Article ID 176395 (2014) 1-7.
8
[9] X.J. Yang, D. Baleanu, and W.P. Zhong, Approximation solutions for diusion equation on Cantor time-space, Proceeding of the Romanian Academy, 14 (2013) 127-133.
9
[10] X.J. Yang, Local fractional integral equations and their applications, Advances in Computer Science and its Applications, 1 (2012) 234-239.
10
[11] X.J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
11
[12] W.P. Zhong, F. Gao, X.M. Shen, Applications of Yang-Fourier transform to local Fractional equations with local fractional derivative and local fractional integral operater, Adv. Mat. Res., 461 (2012) 306-310.
12
ORIGINAL_ARTICLE
Some properties of fuzzy real numbers
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.
https://scma.maragheh.ac.ir/article_18685_8eb1db4d00d23665dcf2e7857784a827.pdf
2016-02-01
21
27
Fuzzy real number
Bernoulli's inequality
Real number
Bayaz
Daraby
bdaraby@maragheh.ac.ir
1
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
AUTHOR
Javad
Jafari
javad.jafari33333@gmail.com
2
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
LEAD_AUTHOR
[1] T. Bag and S.K. Samanta, A comperative study of fuzzy norms on a linear space, Fuzzy Set and Systems, 159(6)(2008), 670-684.
1
[2] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems, 48 (1992), 239-248.
2
[3] M. Mizumoto and K. Tanaka, Some properties of fuzzy numbers, in: M.M. Gupta et al., Eds., Advances in Fuzzy Set Theory and Applications (North-Holland, New York, 1979), 153-164.
3
[4] W. Rudin, Principles of Mathetical Analysis, Mcgraw-Hill, New York, 1976.
4
[5] I. Sadeqi, F. Moradlou, and M. Salehi, On approximate Cauchy equation in Felbins type fuzzy normed linear spaces, to appear in Iran. J. Fuzzy Syst. 10: 3 (2013), 51-63.
5
ORIGINAL_ARTICLE
Some study on the growth properties of entire functions represented by vector valued Dirichlet series in the light of relative Ritt orders
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).
https://scma.maragheh.ac.ir/article_18094_663f26d0249c7fa7dd6e83e21ad32d04.pdf
2016-02-01
29
35
Vector valued
Dirichlet series (VVDS)
Relative Ritt order
Relative Ritt lower order
growth
Sanjib
Datta
sanjib_kr_datta@yahoo.co.in
1
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-\ 741235, West Bengal, India.
LEAD_AUTHOR
Tanmay
Biswas
tanmaybiswas_math@rediffmail.com
2
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
AUTHOR
Pranab
Das
pranabdas90@gmail.com
3
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
AUTHOR
[1] Q.I. Rahaman, The Ritt order of the derivative of an entire function, Annales Polonici Mathematici., 17 (1965) 137-140.
1
[2] C.T. Rajagopal and A.R. Reddy, A note on entire functions represented by Dirichlet series, Annales Polonici Mathematici., 17 (1965) 199-208.
2
[3] J.F. Ritt, On certain points in the theory of Dirichlet series, Amer. Jour. Math., 50 (1928) 73-86.
3
[4] G.S. Srivastava, A note on relative type of entire functions represented by vector valued dirichlet series, Journal of Classicial Analysis, 2(1) (2013) 61-72.
4
[5] G.S. Srivastava and A. Sharma, On generalized order and generalized type of vector valued Dirichlet series of slow growth, Int. J. Math. Archive, 2(12) (2011) 2652-2659.
5
[6] B.L. Srivastava, A study of spaces of certain classes of vector valued Dirichlet series, Thesis, I. I. T., Kanpur, 1983.
6
[7] R.P. Srivastav and R.K. Ghosh, On entire functions represented by Dirichlet series, Annales Polonici Mathematici., 13 (1963) 93-100.
7
ORIGINAL_ARTICLE
Numerical solution of a class of nonlinear two-dimensional integral equations using Bernoulli polynomials
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.
https://scma.maragheh.ac.ir/article_15994_6d676e68a2b7a882c1334cdc50d1acf4.pdf
2016-02-01
37
51
Nonlinear two-dimensional integral equations
Bernoulli polynomials
Collocation method
Operational matrices
Sohrab
Bazm
sbazm@maragheh.ac.ir
1
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
LEAD_AUTHOR
[1] E. Babolian, S. Bazm, and P. Lima, Numerical solution of nonlinear two-dimensional integral equations using rationalized Haar functions, Commun. Nonl. Sci. Numer. Simul. 16(3) (2011) 1164{1175.
1
[2] S. Bazm, Bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations, J. Comput. Appl. Math. 275 (2015) 44-60.
2
[3] A. H. Bhrawy, E. Tohidi, and F. Soleymani, A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-dierential equations with piecewise intervals, Appl. Math. Comput. 219(2) (2012) 482-497.
3
[4] A. Erdelyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Higher Transcen-dental Functions, Vol. III, McGraw-Hill, New York, 1955.
4
[5] H. Guoqiang, K. Hayami, K. Sugihara, and W. Jiong, Extrapolation method of iterated collocation solution for two-dimensional nonlinear Volterra integral equations, App. Math. Comput. 112 (2009) 70-76.
5
[6] E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 1989.
6
[7] P. Lancaster, The Theory of Matrices: With Applications, second ed., Academic Press, New York, 1984.
7
[8] Y.L. Luke, The Special Functions and Their Approximations, Vol. I, Academic Press, New York, 1969.
8
[9] K. Maleknejad, S. Sohrabi, and B. Baranji, Application of 2D-BPFs to nonlinear integral equations, Commun. Nonl. Sci. Numer. Simul. 15 (2010) 527-535.
9
[10] S. Nemati, P.M. Lima, and Y. Ordokhani, Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials, J. Comput. Appl. Math. 242 (2013) 53{69.
10
[11] S. Nemati, and Y. Ordokhani, Solving Nonlinear Two-Dimensional Volterra Integral Equations of the First-kind Using the Bivariate Shifted Legendre Functions, International Journal of Mathematical Modelling & Computations 5(3)
11
(2015) 1-12.
12
[12] A. Tari, M.Y. Rahimi, S. Shahmorad, and F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the dierential transform method, J. Comput. Appl. Math. 228 (2000) 49-61.
13
[13] F. Toutounian and E. Tohidi, A new Bernoulli matrix method for solving second order linear partial dierential equations with the convergence analysis, Appl. Math. Comput. 223 (2013) 298-310.
14
ORIGINAL_ARTICLE
On strongly Jordan zero-product preserving maps
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.
https://scma.maragheh.ac.ir/article_18096_d23368a43afbd4357de9825202e142e0.pdf
2016-02-01
53
61
Strongly zero-product preserving map
Strongly Jordan zero-product preserving map
Zero-product preserving map
Jordan zero-product preserving map
Tensor product
Ali Reza
Khoddami
khoddami.alireza@shahroodut.ac.ir
1
Department of Pure Mathematics, University of Shahrood, P. O. Box 3619995161-316, Shahrood, Iran.
LEAD_AUTHOR
[1] M.A. Chebotar, W.-F. Ke, P.-H. Lee and N.-C. Wong, Mappings preserving zero products , Studia Math., 155 1 (2003), 77-94.
1
[2] H. Ghahramani, Zero product determined triangular algebras , Linear Multilinear Algebra, 61 (2013), 741-757.
2
[3] A.R. Khoddami and H.R.E. Vishki, The higher duals of a Banach algebra induced by a bounded linear functional, Bull. Math. Anal. Appl. 3 (2011), 118-122.
3
[4] A.R. Khoddami, Strongly zero-product preserving maps on normed algebras induced by a bounded linear functional, Khayyam J. Math., 1 (2015), no. 1, 107-114.
4
[5] A.R. Khoddami, On maps preserving strongly zero-products, Chamchuri. J. Math., 7 (2015), 16-23.
5
ORIGINAL_ARTICLE
Parabolic starlike mappings of the unit ball $B^n$
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 $B^n$.
https://scma.maragheh.ac.ir/article_17820_b9493019b43e586b7325e86fcd33c0a4.pdf
2016-02-01
63
70
Roper-Suffridge extention operator
Biholomorphic mapping
Parabolic starlike function
Samira
Rahrovi
sarahrovi@gmail.com
1
Department of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551-761167, Bonab, Iran.
LEAD_AUTHOR
[1] I. Graham and G. Kohr, Univalent mappings associated with the Roper-Suridge extension operator, J. Anal. Math., 81 (2000) 331-342.
1
[2] I. Graham and G. Kohr, An extension theorem and subclasses of univalent mappings in several complex variables, Complex Var., 47 (2002) 59-72.
2
[3] I. Graham and G. Kohr, Geometric function theory in one and higher dimensions, Marcel Dekker, New York, (2003).
3
[4] I. Graham, G. Kohr, and M. Kohr, Loewner chains and the Roper-Suridge Extension Operator, J. Math. Anal. Appl., 247 (2000) 448-465.
4
[5] H. Hamad, T. Honda, and G. Kohr, Parabolic starlike mappings in Several complex variables, Manuscripta math. 123 (2007), 301-324.
5
[6] W. Hengartner and G. Schober, On schlicht mappings to domains convex in one direction, Comment. Math. Helv., 45 (1970), 303-314.
6
[7] J. A. Pfaltzgra and T.J. Suridge, An extension theorem and linear invariant families generated by starlike maps. Ann. Mariae Curie Sklodowska, 53 (1999), 193-207.
7
[8] K.A. Roper and T.J. Suridge, Convex mappings on the unit ball Cn, J. Anal. Math., 65 (1995), 333-347.
8
[9] T.J. Suridge, Starlike and convex maps in Banach spaces, Pac. J. Math., 46 (1973), 474-489.
9