2015
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Some relationship between Gframes and frames
2
2
In this paper we proved that every gRiesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em Gframes as special frames}, Turk. J. Math., 35, (2011) 111]. Also, we derived similar results for gorthonormal and orthogonal bases. Some relationships between dual frame, dual gframe and exact frame and exact gframe are presented too.
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1
7
مهدی
رشیدی کوچی
Mehdi
RashidiKouchi
Department of Mathematics, Islamic Azad University, Kahnooj Branch,
Kahnooj, Iran.
Department of Mathematics, Islamic Azad University
Iran
m_rashidi@kahnoojiau.ac.ir
اکبر
نظری
Akbar
Nazari
Department of Mathematics, Shahid Bahonar University, Kerman, Iran.
Department of Mathematics, Shahid Bahonar
Iran
nazari@mail.uk.ac.ir
Frame
GFrame
Hilbert C*module
gframe operator
Bounded operator
[[1] Askarizadeh A., Dehghan M. A.: , Gframes as special frames, Turk. J. Math., 35, 111 (2011).##[2] Daubechies I., Grossmann A., Meyer Y.:, Painless nonorthogonal expansions, J. Math. Phys. 27, 12711283 (1986).##[3] Duffin R.J., Schaeffer A.C.:, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 ,(1952) 341366.##[4] Frank M., Larson D.R.:, Frames in Hilbert C*modules and C*algebras, J. Operator Theory 48 , 273314 (2002).##[5] Sun W.:, gFrames and gRiesz bases, J. Math. Anal. Appl., 322, 437452 (2006).##[6] Zhu Y. C.: , Characterization of gframes and gRiesz bases in Hilbert space, Acta Mathematica Sinica, 2410, 17271736 (2008).##]
Comparison of acceleration techniques of analytical methods for solving differential equations of integer and fractional order
2
2
The work addressed in this paper is a comparative study between convergence of the acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method and Adomian decomposition method for solving differential equations of integer and fractional orders.
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9
17


H. R.
Marasi
Department of Mathematics, University of Bonab, Bonab, Iran.
Department of Mathematics, University of
Iran
hamidreza.marasi@gmail.com


M.
Daneshbastam
Department of Mathematics, University of Bonab, Bonab, Iran.
Department of Mathematics, University of
Iran
daneshmojtaba79@gmail.com
Adomiam decomposition method
Homotopy analysis method
Acceleration technique
shanks transorm
Pade approximant
[[1] G.C. Wu, Y.G. Shi, K.T. Wu, Adomian decomposition method and nonanalytical solutions of fractional dierential equations, Romanian J. Phys. 56 (2011) 873880. ##[2] M. Ganjiani, Solution of nonlinear fractional dierential equations using homotopy analysis method, Applied Mathematical Modelling 34(2010)16341641. ##[3] S.J. Liao, Beyond perturbation: introduction to homotopy analysis method, Boca Raton. FL, Chapman and Hall, 2004. ##[4] S. J. Liao, The proposed homotipy analysis method technique for the solution of nonlinear problems, PhD dissertation, Shanghai Jiao Tong University(1992). ##[5] G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135, 501544 (1988) ##[6] H.R. Marasi, M. Nikbakht, Adomian decompositiom method for boundary value problems, Aus. J. Basic. Appl. Sci. 5, 21062111(2011) ##[7] H.R. Marasi, S. Karimi, Convergence of variational iteration method for solving fractional KleinGordon equation (accepted). ##[8] JunSheng Duan , Temuer Chaolu, Randolph Rach , Lei Lu,The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional dierential equation.Comput.Math. Appl.66 (2013) 728736 ##[9] F. Abidi, K. Omrani, The homotopy analysis method for solving the FornbergWhitham equation and com parison with Adomians decomposition method, Comput. Math. Appl. 59 (2010) 27432750.##]
Superstability of $m$additive maps on complete nonArchimedean spaces
2
2
The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$additive maps on complete nonArchimedean spaces via a fixed point method raised by Diaz and Margolis.
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19
25


Ismail
Nikoufar
Department of Mathematics, Payame Noor University, P.O. Box 193953697 Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
nikoufar@pnu.ac.ir
Superstability
Complete nonArchimedean spaces
$m$additive functional equation
[[1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 6466. ##[2] R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006), no. 1, 167173. ##[3] J. Baker, J. Lawrence and F. Zorzitto, The stability of the equation $f(x + y) =f(x)f(y)$, Proc. Am. Math. Soc. 74 (1979), 242246 ##[4] D.G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math, Soc. 57 (1951), 223237. ##[5] L. C$breve{a}$dariu and V. Radu, On the stability of the Cauchy functional equation: A fixed point approach,##Grazer Math. Ber. {346} (2004), 4352. ##[6] J.B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on the generalized complete metric space, Bull. Amer. Math. Soc. {126} (1968) 305309. ##[7] A. Ebadian, I. Nikoufar, Th. M. Rassias, and N. Ghobadipour, Stability of generalized derivations on Hilbert C*modules associated to a Pexiderized CauchyJensen type functional equation, Acta Mathematica Scientia, {32B}(3) (2012), 12261238. ##[8] P. Gu{a}vruta, A generalization of the HyersUlamRassias stability of approximately additive mappings,##J. Math. Anal. Appl. {184} (1994), 431436. ##[9] P. Gu{a}vruta, An answer to a question of J. M. Rassias concerning the stability of Cauchy equation,##in: Advances in Equations and Inequalities, Hardronic Math. Ser. (1999), 6771. ##[10] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. {27} (1941), 222224. ##[11] D.H. Hyers, G. Isac, and Th. M. Rassias, Stability of functional equations in several variables, Birkh"{a}user, Boston, 1998. ##[12] D.H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequations Math., 44 (1992), 125153. ##[13] I. Nikoufar and Th.M. Rassias, Approximately algebraic tensor products, to appear in Miskolc Mathematical Notes. ##[14] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. {72} (1978), 297300. ##[15] J.M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. {46} (1982), 126130. ##[16] V. Radu, The fixed point alternative and the stability of functional equations, Sem. Fixed Point Theory {4}(1) (2003) 9196. ##[17] S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, Interscience Publisher, New York, 1960.##]
Analytical solutions for the fractional Fisher's equation
2
2
In this paper, we consider the inhomogeneous timefractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified Homotopy perturbation method, it is possible to get an exact solution.
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27
49


H.
Kheiri
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Faculty of Mathematical Sciences, University
Iran
hkheiri@tabrizu.ac.ir
آ.
مجاور
A.
Mojaver
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Faculty of Mathematical Sciences, University
Iran
aida_mojaver1987@yahoo.com


S.
Shahi
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Faculty of Mathematical Sciences, University
Iran
samane sh7@yahoo.com
Fractional Fisher's equation
MittagLeffer
Method of separating variables
[[1] Adomian, G., Stochastic SystemsAcademic Press, New York, 1983.##[2] Adomian, G., A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Model., 13 (7) (1992) 17.##[3] Dimovski, I., Convolutional calculus, Publishing House of the Bulgarian Academy of Sciences, 1982.##[4] Duan, J.S., Rach, R., A new modification of the adomian decomposition method for solving boundary value##problems for higher order nonlinear differential equations, Appl. Math. Comput., 218 (2011) 40904118.##[5] He, J. H., homotipy perturbation technique, Comput. Methods Appl. Mech. Engrg., 178 (1999) 257262.##[6] He, J. H., A coupling method of homotopy tecknique and perturbation tecknique for nonlinear problems, Int. J.##Nonlinear Mech., 35 (2000) 3743. ##[7] Hilfer, R., Applications of Fractional Calculus in PhysicsWorld Scientific, Singapore, 2000.##[8] S. IrandoustPakchin, H. Kheiri, S. AbdiMazraeh, Efficient computational algorithms for solving one class of fractional boundary value problems, Comp. Math. Math Phys., 53 (7) (2013) 920932.##[9] Kumar, M., Singh, N., Modified Adomian Decomposition Method and computer implementation for solving singular##boundary value problems arising in various physical problems, Comput. and Chem. Eng., 34 (2010) 17501760.##[10] Liao, S. J., on the proposed homotopy analysis technique for nonlinear problems and its applications, Ph.D. Dissertation. Shanghai Jiao Tong University, Shanghai, 1992. ##[11] Liao, S. J., On the homotopy analysis method for nonlinear problems, Appl. Math. Comput., 147 (2004) 499513. ##[12] Luchko, Y. and Gorenflo, R., An operational method for solving fractional differential equations with the caputo derivatives, Acta Math. Vietnam, 24(2) (1999) 207233.##[13] Odibat, Z. and Momani, S., Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos Soliton Frac., 36 (2008) 16774.##[14] Odibat, Z. and Momani, S., Application of variational iteration method to nonlinear differential equation of fractional order, Int. J. Nonlinear Sci. Numer. Simul., 1(7) (2006) 2719.##[15] Odibat, Z. and Momani, S., Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Soliton Frac., 31 (2007) 124855.##[16] Podlubny, I., Fractional Differential Equations, Academic Press, New York, NY, USA, 1999.##[17] Reich, S., Constructive techniques for accretive and monotone operators in Applied Nonlinear Analysis, Academic Press, New York, 1979, 335345.##[18] Rus, I. A., Petruşel, A. and Petruş, G., Fixed Point Theory: 1950  2000, Romanian Contribution, House of the##Book of Science, ClujNapoca, 2002.##[19] Sabatier, J., Agrawal, O. P. and Machado, J. A. T., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.##[20] Samko, S., Kilbas, A., and Marichev, O., Fractional integrals and derivatives: theory and applications, USA: Gordon and breach science publishers, 1993.##[21] YepezMartinez, H., Reyes, J. M. and Sosa, I. O., Analytical solutions to the fractional Fisher equation by applying the fractional Subequation method, British Journal of Mathematics & Computer Science, 4 (11) (2014).##[22] Zhang, X. and Liu, J., An analytic study on timefractional Fisher's equation by using HPM, Walailak Journal of Science and Technology (WJST), 11 (12) (2014).##]
Weighted composition operators between growth spaces on circular and strictly convex domain
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2
Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$f(x)leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the Minkowski functional on $Omega_X$ and $omega :[0,1)rightarrow(0,infty)$ is a nondecreasing, continuous and unbounded function. Boundedness and compactness of weighted composition operators between growth spaces on circular and strictly convex domains were investigated.
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51
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Shayesteh
Rezaei
Department of Pure Mathematics, Aligudarz Branch, Islamic Azad
University, Aligudarz, Iran.
Department of Pure Mathematics, Aligudarz
Iran
sh.rezaei@iaualigudarz.ac.ir
Weighted composition operator
Growth space
Circular domain
[[1] E. Abakumov and E. Doubtsov,Reverse estimates in growth spaces, Mathematische Zeitschrift, 271 (2012) 392413.##[2] l K. D. Bierstedt, J. Bonet and J. Taskinen, Associated weights and spaces of holomorphic functions, Studia Math. 127 (2) (1998) 137168.##[3] l J. Bonet, P. Domanski, M. Lindstrom and J. Taskinen, Composition operators between weighted Banach spaces of analytic functions, J. Aust. Math. Soc. (Ser. A),64 (1998) 101118.##[4] lJ. B. Conway,A Course in Functional Analysis, SpingerVerlag New York, 1985. ##[5] E. Doubstov, Growth spaces on circular domains: Composition operators and Carleson measure, Comptes Rendus Mathematigue, 347 (2009), 609611.##[6] E. Doubtsov, CarlesonSobolev measure for weighted Bloch spaces, Func. Anal. 258 (2010) 28012816.##[7] E. S. Dubtsov, Weighted composition operators on growth spaces, Siberian Mathematical Journal, 50 ( 6) (2009) 9981006.##[8] W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc., 51 (1995) 309320.##[9] A. MontesRodrguez,Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc., 61 (2) (2000) 872884.##[10] J. Mujica, Complex Analysis in Banach Spaces, Elsevier Science Publishing Company, 1985.##[11] G. Patrizio, Parabolic exhaustions for strictly convex domains, Manuscripta Math. 47 (1984) 271309.##[12] E. Zeidler, Applied Functional Analysis Applications to Mathematical Physics, Applied Mathematical Sciences, SpringerVerlag New Yorc Inc. V. 108.##]
Convergence analysis of product integration method for nonlinear weakly singular VolterraFredholm integral equations
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2
In this paper, we studied the numerical solution of nonlinear weakly singular VolterraFredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear VolterraFredholm integral equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.
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57
69


Parviz
Darania
Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 165, UrmiaIran
Department of Mathematics, Faculty of Science,
Iran
p.darania@urmia.ac.ir


Jafar
Ahmadi Shali
Department of Mathematics and Computer Science, University of Tabriz, TabrizIran
Department of Mathematics and Computer Science,
Iran
j ahmadishali@tabrizu.ac.ir
VolterraFredholm integral equations
Product integration method
Convergence analysis
[[1] P. Linz, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia(1985). ##[2] N. Levinson, A nonlinear Volterra equations arising in the theory of superuidity, J. Math. Anal. Appl. 1 (1960) 111. ##[3] A. Pedas and E.Tamme, Fully discrete Galerkin method for Fredholm integrodierential equations with weakly singular kernels, Computational Methods in Applied Mathematics, Vol 8 No 3 (2008) 294308. ##[4] T. Tang, S. McKee and T. Diogo, product integration method for an integral equation with logarithmic singular kernel, App. Numer. Math. 9 (1992), 259266. ##[5] M. Rasty and M. Hadizadeh, A Product integration approach on new orthogonal poly nomials for nonlinear weakly singular integral equations, Acta Appl. Math. 109 (2010), 861873. ##[6] A.P. Orsi, Product integration for Volterra integral equations of the second kined with weakly singular kernels, Math. Comput. 212 (1996), 12011212. ##[7] H. Brunner, Highorder collocation methods for singular Volterra functional equations of neutral typr, Applied Numerical Mathematics, 57 (2007) 533548. ##[8] H. Brunner, The numerical solution of weakly singular Volterra functional integrodierential equations with variable delays, Comm. Pure Appl. Anal. 5 (2006) 261276. ##[9] J.B. Keller and W.E. Olmstead, Temperature of nonlinear radiating semiinnite solid, Q. Appl. Math. 29 (1972) 559566. ##[10] V.S. Chelyshkov, Alternative orthogonal polynomials and quadratures, Electron. Trans. Numer. Anal. 25(7), (2006), 1726. ##[11] H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge Monographs on Applied and Computational Mathematics, vol. 15, Cambridge University Press, Cambridge, 2004. ##[12] R. P. Kanwal and K. C. Liu, A Taylor expansion approach for solving integral equations, Int. J. Math. Educ. Sci. Technol. 3 (1989), 411414. ##[13] G. Criscuolo, G. Mastroianni and G. Monegato, Convergence properties of a class of product formulas for weakly singular integral equations, Math. Comput. 55 (1990), 213230. ##[14] P. Nevai, Mean convergence of Lagrange interpolation. III. Trans. Am. Math. Soc. 282 (1984), 669689. ##[15] H. Kaneko and Y.Xu, Gausstype quadratures for weakly singular integrals and their application to Fredholm integral equations of second kind. Math. Comput. 62, (1994) 739753. ##[16] V.I. Krylov, Approximate Calculation of Integrals. Macmillan Company, New York (1962). ##[17] P.K. Kythe and P. Puri, Computational Methods for Linear Integral Equations. Birkhuser, Boston (2002).##]
Composition operators acting on weighted Hilbert spaces of analytic functions
2
2
In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and observed that a formula for the essential norm, gives a HilbertSchmidt characterization and characterizes the membership in Schattenclass for these operators. Also, closed range composition operators are investigated.
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71
79


Mostafa
Hassanlou
Shahid Bakeri High Education Center of Miandoab, Urmia University,
Urmia, Iran.
Shahid Bakeri High Education Center of Miandoab,
Iran
m_hasanloo@tabrizu.ac.ir
Composition operators
Weighted analytic space
HilbertSchmidt
Schattenclass
[[1] C.C. Cowen and B.D. Maccluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995.##[2] K. Kellay and P. Lefevre, Compact composition operators on weighted Hilbert spaces of analytic functions, J. Math. Anal. Appl. 386 (2012), 718727.##[3] M. Lindstrom and E. Wolf, Essential norm of the dierence of weighted composition opera tors, Monatsh. Math. 153 (2008), 133143.##[4] D. Luecking, Trace ideal criteria for Toeplitz operators, J. Funct. Anal. 73 (1987), 345368.##[5] W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc. 51 (1995), 309320.##[6] J. Pau and P.A. Perez, Composition operators acting on weighted Dirichlet spaces, J. Math. Anal. Appl. 401 (2012), 682694.##[7] J.H. Shapiro, Composition operator and classical function theory, SpringerVerlag, New York, 1993.##[8] M. Wang, Weighted composition operators between Dirichlet spaces, Acta Math. Sci. 31B(2) (2011), 641651.##[9] K. Zhu, Schatten class composition operators on weighted Bergman spaces of the disk, J. Operator Theory 46 (2001), 173181.##[10] K. Zhu, Spaces of holomorphic functions in the unit ball, Springer, New York, 2005.##[11] K. Zhu, Operator Theory in Function Spaces, Second Edition, Math. Surveys and Monographs, Vol. 138, American Mathematical Society: Providence, Rhode Island, 2007.##]