Generalized slow growth of special monogenic functions

• Autorzy: Kumar S.

Identyfikatory

DOI

10.1515/jaa-2016-0007

• Języki publikacji: EN

Abstrakty

EN

In the present paper we study the generalized slow growth of special monogenic functions. The characterizations of generalized order, generalized lower order, generalized type and generalized lower type of special monogenic functions have been obtained in terms of their Taylor series coefficients.

Słowa kluczowe

EN

generalized Cauchy–Riemann system; special monogenic function; maximum term; central index; generalized growth

PL

równanie Cauchy'ego-Riemanna; specjalna funkcja monogeniczna

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2016
• Tom: Vol. 22, nr 1
• Strony: 67--79
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kumar S.

• Department of Mathematics, Jaypee University of Engineering and Technology, Guna – 473226 (M. P.), India

Bibliografia

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• [3] M. A. Abul-Ez and R. De Almeida, On the lower order and type of entire axially monogenic function, Results Math. 63 (2013), 1257-1275.
• [4] R. De Almeida and R. S. Krausshar, On the asymptotic growth of entire monogenic functions, Z. Anal. Anwend. 24 (2005), no. 4, 791-813.
• [5] D. Constates, R. De Almeida and R. S. Krausshar, On the growth type of entire monogenic functions, Arch. Math. (Basel) 88 (2007), 153-163.
• [6] D. Constales, R. De Almeida and R. S. Krausshar, On the relation between the growth and the Taylor coefficients of entire solutions to the higher dimensional Cauchy-Riemann system in Rn+1, J. Math. Anal. App. 327 (2007), 763-775.
• [7] V. G. Iyer, A property of the maximum modulus of integral functions, J. Indian Math. Soc. (N. S.) 6 (1942), 69-80.
• [8] G. P. Kapoor and A. Nautiyal, Polynomial approximation of an entire function of slow growth, J. Approx. Theory 32 (1981), 64-75.
• [9] 5. Kumar, Generalized growth of special monogenic functions, J. Complex Anal. 2014 (2014), Article ID 510232.
• [10] S. Kumar and K. Bala, Generalized type of entire monogenic functions of slow growth, Transylv. J. Math. Mech. 3 (2011), no. 2, 95-102.
• [11] S. Kumar and K. Bala, Generalized order of entire monogenic functions of slow growth, J. Nonlinear Sci. Appl. 5 (2012), no. 6, 418-425.
• [12] S. Kumar and K. Bala, Generalized growth of monogenic Taylor series of finite convergence radius, Ann. Univ. Ferrara Sez. VII Sci. Mat. 59 (2013), no. 1, 127-140.
• [13] S. Kumar and G. S. Srivastava, Maximum term and lower order of entire functions of several complex variables, Bull. Math. Anal. Appl. 3 (2011), no. 1, 156-164.
• [14] S. Kumar and G. S. Srivastava, On the maximum term and lower order of entire monogenic functions, Transylv. J. Math. Mech. 6 (2014), no. 1, 29-38.
• [15] M. N. Seremeta, On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. Ser. 2 88 (1970), 291-301.
• [16] G. S. Srivastava and S. Kumar, On the generalized order and generalized type of entire monogenic functions, Demonstr. Math. 46 (2013), no. 4, 663-677.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.