Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc

In this paper we introduce the notion of relative $(p,q,t)L$-th order, relative $(p,q,t)L$-th type, and relative $(p,q,t)L$-th weak type of meromorphic functions in the unit disc with respect to an entire functions where $p,q\in \mathbb{N} $ and $t\in \mathbb{N} \cup \left\{ -1,0\right\} $ and then investigate some basic properties of it.

Keywords:

Meromorphic function, unit disc, unit disc Property (D),

PDF

___

[1] Bernal, L., Crecimiento relativo de funciones enteras. Contribuci´on al estudio de lasfunciones enteras con ´ındice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
[2] Bernal, L., Orden relativo de crecimiento de funciones enteras, Collect. Math. Vol: 39 (1988), 209-229.
[3] Fenton, P. C. and Rossi, J., ODEs and Wiman–Valiron theory in the unit disc, J. Math. Anal. Appl., Vol: 367 (2010), 137-145.
[4] Girnyk, M. A., On the inverse problem of the theory of the distribution of values for functions that are analytic in the unit disc, (Russian) Ukrain. Mat. Z., Vol: 29, No. 1 (1977), 32-39.
[5] Hayman, W.K., Meromorphic Functions,Oxford Mathematical Monographs. Clarendon Press, Oxford (1964).
[6] Juneja, O. P., Kapoor, G. P. and Bajpai, S. K., On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., Vol: 282 (1976), 53-67.
[7] Juneja, O. P. and Kapoor, G. P., Analytic functions-growth aspects. Research Notes in Mathematics 104, Pitman Adv. Publ. Prog., Boston-London- Melbourne, 1985.
[8] Kapoor, G. P. and Gopal, K., Decomposition theorems for analytic functions having slow rates of growth in a finite disc. J. Math. Anal. Appl. Vol: 74, (1980), 446-455.
[9] Laine, I., Complex differential equations. Handbook of differential equations: ordinary differential equations, Vol: IV, 269-363, Handb. Differ. Equ., Amsterdam: Elsevier/North-Holland, 2008.
[10] Li, Y. Z., On the growth of the solution of two-order differential equations in the unit disc, Pure Appl. Math., Vol: 4 (2002), 295-300.
[11] Nicholls, P. J. and Sons, L. R., Minimum modulus and zeros of functions in the unit disc. Proc. Lond.Math. Soc., Vol: 31 (3) (1975), 99-113.
[12] Somasundaram, D. and Thamizharasi, R., A note on the entire functions of L-bounded index and L-type, Indian J. Pure Appl.Math., Vol: 19, No. 3, (1988), 284-293.
[13] Sons, L. R., Unbounded functions in the unit disc, Internat. J. Math. & Math. Sci., Vol: 6, No. 2 (1983), 201-242.
[14] Tsuji, M., Potential Theory in Modern Function Theory, Chelsea, New York, (1975), reprint of the 1959 edition.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

Arşiv