Research Article
BibTex RIS Cite

Further study on the results of Sheremeta

Year 2019, Volume: 68 Issue: 1, 1007 - 1018, 01.02.2019
https://doi.org/10.31801/cfsuasmas.501439

Abstract

In this paper we estimate some growth rates of composite entire and meromorphic functions in the light of their relative (p,q)-th order and relative (p,q)-th lower order which considerably extend some results of Sheremeta [14].

References

  • 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.
  • Bernal, L., Orden relative de crecimiento de funciones enteras , Collect. Math., 39 (1988), 209-229.
  • Bergweiler, W., On the Nevanlinna Characteristic of a composite function, Complex Variables Theory Appl. , 10 (2-3) (1988), 225-236.
  • Bergweiler, W., On the growth rate of composite meromorphic functions, Complex Variables Theory Appl. , 14 (1-4) (1990), 187-196.
  • Clunie, J., The composition of entire and meromorphic functions, In: Mathematical essays dedicated to A.J.Macintyre, Ohio University Press, (1970), 75 - 92.
  • Debnath, L., Datta, S. K., Biswas T. and Kar, A., Growth of meromorphic functions depending on (p,q)-th relative order, Facta Univ. Ser. Math. Inform., 31 (3) (2016), 691-705.
  • Datta, S. K., Biswas T. and Biswas, C., Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, International J. of Math. Sci. & Engg. Appls. (IJMSEA), 8 (IV) (2014), 207-218.
  • Hayman, W.K., Meromorphic Functions, The Clarendon Press, Oxford (1964).
  • 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., 282, (1976), 53-67.
  • Laine, I., Nevanlinna Theory and Complex Differential Equations. De Gruyter, Berlin, 1993.
  • Lahiri B. K. and Banerjee, D., Relative order of entire and meromorphic functions, Proc. Nat. Acad. Sci. India Ser. A., 69(A) (3) (1999), 339-354.
  • Ruiz, L. M. S., Datta, S. K., Biswas T. and Mondal, G. K., On the (p,q)-th relative order oriented growth properties of entire functions, Abstr. Appl. Anal., 2014, Art. ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
  • Sato, D., On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), 411-414.
  • Sheremeta, M. M., On the growth of a composite entire functions, Carpathian Math. Publ.,9 (2) (2017), 181--187.
  • Titchmarsh, E. C., The Theory of Functions, 2nd ed. Oxford University Press, Oxford , (1968).
  • Yang C. C. and Yi, H. X., Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
  • Yang, L., Value distribution theory, Springer-Verlag, Berlin, 1993.
  • Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.
Year 2019, Volume: 68 Issue: 1, 1007 - 1018, 01.02.2019
https://doi.org/10.31801/cfsuasmas.501439

Abstract

References

  • 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.
  • Bernal, L., Orden relative de crecimiento de funciones enteras , Collect. Math., 39 (1988), 209-229.
  • Bergweiler, W., On the Nevanlinna Characteristic of a composite function, Complex Variables Theory Appl. , 10 (2-3) (1988), 225-236.
  • Bergweiler, W., On the growth rate of composite meromorphic functions, Complex Variables Theory Appl. , 14 (1-4) (1990), 187-196.
  • Clunie, J., The composition of entire and meromorphic functions, In: Mathematical essays dedicated to A.J.Macintyre, Ohio University Press, (1970), 75 - 92.
  • Debnath, L., Datta, S. K., Biswas T. and Kar, A., Growth of meromorphic functions depending on (p,q)-th relative order, Facta Univ. Ser. Math. Inform., 31 (3) (2016), 691-705.
  • Datta, S. K., Biswas T. and Biswas, C., Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, International J. of Math. Sci. & Engg. Appls. (IJMSEA), 8 (IV) (2014), 207-218.
  • Hayman, W.K., Meromorphic Functions, The Clarendon Press, Oxford (1964).
  • 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., 282, (1976), 53-67.
  • Laine, I., Nevanlinna Theory and Complex Differential Equations. De Gruyter, Berlin, 1993.
  • Lahiri B. K. and Banerjee, D., Relative order of entire and meromorphic functions, Proc. Nat. Acad. Sci. India Ser. A., 69(A) (3) (1999), 339-354.
  • Ruiz, L. M. S., Datta, S. K., Biswas T. and Mondal, G. K., On the (p,q)-th relative order oriented growth properties of entire functions, Abstr. Appl. Anal., 2014, Art. ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
  • Sato, D., On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), 411-414.
  • Sheremeta, M. M., On the growth of a composite entire functions, Carpathian Math. Publ.,9 (2) (2017), 181--187.
  • Titchmarsh, E. C., The Theory of Functions, 2nd ed. Oxford University Press, Oxford , (1968).
  • Yang C. C. and Yi, H. X., Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
  • Yang, L., Value distribution theory, Springer-Verlag, Berlin, 1993.
  • Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.
There are 18 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Tanmay Biswas This is me 0000-0001-6984-6897

Publication Date February 1, 2019
Submission Date February 19, 2018
Acceptance Date June 4, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Biswas, T. (2019). Further study on the results of Sheremeta. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 1007-1018. https://doi.org/10.31801/cfsuasmas.501439
AMA Biswas T. Further study on the results of Sheremeta. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):1007-1018. doi:10.31801/cfsuasmas.501439
Chicago Biswas, Tanmay. “Further Study on the Results of Sheremeta”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 1007-18. https://doi.org/10.31801/cfsuasmas.501439.
EndNote Biswas T (February 1, 2019) Further study on the results of Sheremeta. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 1007–1018.
IEEE T. Biswas, “Further study on the results of Sheremeta”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 1007–1018, 2019, doi: 10.31801/cfsuasmas.501439.
ISNAD Biswas, Tanmay. “Further Study on the Results of Sheremeta”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 1007-1018. https://doi.org/10.31801/cfsuasmas.501439.
JAMA Biswas T. Further study on the results of Sheremeta. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1007–1018.
MLA Biswas, Tanmay. “Further Study on the Results of Sheremeta”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 1007-18, doi:10.31801/cfsuasmas.501439.
Vancouver Biswas T. Further study on the results of Sheremeta. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):1007-18.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.