Hyper Relative Order (p, q) of Entire Functions

Banerjee, Dibyendu; Batabyal, Saikat

doi:10.1515/awutm-2017-0015

Abstract

After the works of Lahiri and Banerjee [6] on the idea of relative order (p, q) of entire functions, we introduce in this paper hyper relative order (p, q) of entire functions where p, q are positive integers with p>q and prove sum theorem, product theorem and theorem on derivative.

References

[1] W. Bergweiler, G. Jank, and L. Volkmann, Wachstumsverhalten Zusammengesetzter Funktionen, Results in Mathematics, 7, (1984), 35–53.10.1007/BF03322486
Search in Google Scholar Back to article
[2] L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math., 39, (1988), 209-229.
Search in Google Scholar Back to article
[3] J. Clunie, The composition of entire and meromorphic functions, Mathematical Esays dedicated to Macintyre, (1970), 75–92.
Search in Google Scholar Back to article
[4] S. K. Datta and R. Biswas, A special type of differential polynomial and its comparative growth properties, International Journal of Modern Engineering Research, 3(5), (2013), 2606-2614.
Search in Google Scholar Back to article
[5] B. K. Lahiri and Dibyendu Banerjee, Generalized relative order of entire functions, Proc. Nat. Acad. Sci. India, 72(A) (IV), (2002), 351-371.
Search in Google Scholar Back to article
[6] B. K. Lahiri and Dibyendu Banerjee, Entire functions of relative order (p,q), Soochow Journal of Mathematics, 31 (4), (2005), 497–513.
Search in Google Scholar Back to article
[7] O. P. Juneja, G. P. Kapoor, and S. K. Bajpai, On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., 282, (1976), 53-67.10.1515/crll.1976.282.53
Search in Google Scholar Back to article
[8] O. P. Juneja, G. P. Kapoor, and S. K. Bajpai, On the (p,q)-type and lower (p,q)-type of an entire function, J. Reine Angew. Math., 290, (1977), 180-190.10.1515/crll.1977.290.180
Search in Google Scholar Back to article
[9] H. S. Kasana, Existence theorem for proximate type of entire functions with index pair (p,q), Bull. Aus. Math. Soc., 35, (1987), 35-42.10.1017/S0004972700013010
Open DOI Search in Google Scholar Back to article
[10] H. S. Kasana, On the coefficients of entire functions with index pair (p,q), Bull. Math., 32(80) (3), (1988), 235-242.
Search in Google Scholar Back to article
[11] H. S. Kasana, The generalized type of entire functions with index pair (p,q), Comment. Math., 2, (1990), 215-222.
Search in Google Scholar Back to article
[12] B. J. Levin, Distribution of zeros of entire functions, American Mathematical Society, publ Providence, 1980.
Search in Google Scholar Back to article
[13] F. Lu and J. Qi, A note on the hyper order of entire functions, Bull. Korean Math. Soc., 50 (4), (2013), 1209-1219.10.4134/BKMS.2013.50.4.1209
Open DOI Search in Google Scholar Back to article
[14] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69, (1963), 411-414.10.1090/S0002-9904-1963-10951-9
Search in Google Scholar Back to article
[15] E. C. Titchmarsh, The theory of functions, 2nd ed., University Press, Oxford, 1968.
Search in Google Scholar Back to article

Hyper Relative Order (p, q) of Entire Functions

Abstract

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