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Year 2019, Volume: 7 Issue: 1, 146 - 167, 15.04.2019

Abstract

References

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  • [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.

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

Year 2019, Volume: 7 Issue: 1, 146 - 167, 15.04.2019

Abstract

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.

References

  • [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.
There are 14 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Tanmay Biswas

Publication Date April 15, 2019
Submission Date May 4, 2018
Acceptance Date March 18, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Biswas, T. (2019). Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc. Konuralp Journal of Mathematics, 7(1), 146-167.
AMA Biswas T. Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc. Konuralp J. Math. April 2019;7(1):146-167.
Chicago Biswas, Tanmay. “Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 146-67.
EndNote Biswas T (April 1, 2019) Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc. Konuralp Journal of Mathematics 7 1 146–167.
IEEE T. Biswas, “Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc”, Konuralp J. Math., vol. 7, no. 1, pp. 146–167, 2019.
ISNAD Biswas, Tanmay. “Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc”. Konuralp Journal of Mathematics 7/1 (April 2019), 146-167.
JAMA Biswas T. Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc. Konuralp J. Math. 2019;7:146–167.
MLA Biswas, Tanmay. “Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 146-67.
Vancouver Biswas T. Some Study on Slowly Changing Function Based Relative Growth of Meromorphic Function in the Unit Disc. Konuralp J. Math. 2019;7(1):146-67.
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