Document Type: Research Paper

Authors

1 Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.

2 Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.

Abstract

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

Keywords

Main Subjects

[1] L. Bernal, Crecimiento relativo de funciones enteras. Contribucion al estudio de lasfunciones enteras conindice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.

[2] L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp. 209-229.

[3] S.K. Datta and T. Biswas, Growth of entire functions based on relative order, Int. J. Pure Appl. Math., Vol. 51, No. 1 (2009), pp. 49-58.

[4] S.K. Datta and A. Biswas, On relative type of entire and meromorphic functions, Advances in Applied Mathematical Analysis, Vol. 8, No. 2 (2013), pp. 63-75.

[5] S.K. Datta and T. Biswas, Relative order of composite entire functions and some related growth properties, Bull. Cal. Math. Soc., Vol. 102, No.3 (2010) pp.259-266.

[6] S.K. Datta, T. Biswas and R. Biswas, Comparative growth properties of composite entire functions in the light of their relative order, The Mathematics Student, Vol. 82, No. 1-4 (2013), pp. 1-8.

[7] S.K. Datta, T. Biswas, and R. Biswas, On relative order based growth estimates of entire functions, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 7, No. II (March, 2013), pp. 59-67.

[8] S.K. Datta, T. Biswas, and D.C. Pramanik, On relative order and maximum term -related comparative growth rates of entire functions, Journal of Tripura Mathematical Society, Vol. 14 (2012), pp. 60-68.

[9] S.K. Datta, T. Biswas, and C. Ghosh, Growth analysis of entire functions concerning generalized relative type and generalized relative weak type, Facta Universitatis (NIS) Ser. Math. Inform, Vol. 30, No. 3 (2015), pp. 295-324.

[10] S.K. Datta and A. Jha, On the weak type of meromorphic functions, Int. Math. Forum, Vol. 4, No. 12(2009), pp. 569-579.

[11] B.K. Lahiri and D. Banerjee, Generalised relative order of entire functions, Proc. Nat. Acad. Sci. India, Vol. 72(A), No. IV (2002), pp. 351-271.

[12] C. Roy, Some properties of entire functions in one and several complex variables, Ph.D. Thesis, submitted to University of Calcutta, 2009.

[13] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., Vol. 69 (1963), pp. 411-414.

[14] E.C. Titchmarsh, The theory of functions, 2nd ed. Oxford University Press, Oxford, (1968).

[15] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, (1949).