Year 2016,
Volume: 4 Issue: 4, 306 - 321, 31.12.2016
Sanjib Kumar Datta
Tanmay Biswas
Debasmita Dutta
References
- L. Bernal : Crecimiento relativo de funciones enteras. Contribución al estudio de lasfunciones enteras con13 ̆053'fndice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
- L. Bernal : Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp.209-229.
- N. Bhattacharjee and I. Lahiri : Growth and value distribution of differential polynomials, Bull. Math. Soc. Sc. Math. Roumanie Tome, Vol. 39(87), No.1-4(1996), pp.85-104.
- W. Bergweiler : On the Nevanlinna characteristic of a composite function, Complex Variables, Vol. 10 (1988), pp. 225-236.
- W. Doeringer : Exceptional values of differential polynomials, Pacific J. Math.,Vol 98, No.1(1982), pp.55-62.
- S. K. Datta : On the order and type of differential monomials, Journal of Pure Mathematics, C.U., Vol.19 (2002), pp.13-17.
- S. K. Datta : On the generalized order and generalized type of differential monomials and differential polynomials, Journal of Mechanics of Continua and Mathematical Sciences, Vol. 2, No. 1 (2007), pp.71-79,
- S. K. Datta and S. Kar : On the growth of differential monomials, International Journal of Pure and Applied Mathematics (IJPAM), Vol. 45, No. 4 (2008), pp.573-585.
- S. K. Datta and S. Kar : Some comparative growth properties of differential polynomials, International Journal of Mathematical Sciences and Engineering Applications (IJMSEA), Vol. 3, No. 1 (2009), pp.113-128.
- S. K. Datta and T. Biswas : On the growth of differential polynomials, Wesleyan Journal of Research, Vol. 2, No. 2 (2009), pp.27-37.
- S. K. Datta and A. R. Das : Some results on the growth properties of differential monomials, International Mathematical Forum, Vol. 4, No. 38 (2009), pp.1863-1876.
- S. K. Datta and E. Jerin : On the growth estimates of differential monomials and differential polynomials generated by meromorphic functions, Journal of Mathematics, N.B.U., Vol. 3 No. 1 (2010), pp.33-52.
- S. K. Datta and A. R. Das : Derivation of some results of maximum terms of differential monomials generated by entire functions, Wesleyan Journal of Research, Vol. 4, No. 1 (2011 ) pp. 15-21.
- S. K. Datta, A. R. Das and A. R. Maji : Maximum terms of differential monomials generated by entire functions, International Journal of Mathematical Sciences and Engineering Applications (IJMSEA), Vol. 5, No. IV (July, 2011), pp.353-359.
- S. K. Datta and A. R. Maji : On different kinds of orders and types of differential monomials generated by transcendental entire functions using their minimum modulus, International Journal of Contemporary Mathematical Sciences, Vol. 6 , No. 42 (2011), pp. 2057 - 2074.
- S. K. Datta and A. R. Maji : On different kinds of orders and types of differential polynomials generated by entire functions using their minimum modulus, International Journal of Mathematical Analysis, Vol. 5, No. 43 (2011), pp. 2127 - 2140.
- S. K. Datta and A. R. Das : Estimation of growth properties of differential polynomials generated by entire functions on the basis of their maximum terms, Review Bulletin of the Calcutta Mathematical Society, Vol. 19, No. 2 (2011), pp. 193-200.
- S. K. Datta and T. Biswas : On a result of Bergweiler, International Journal of Pure and Applied Mathematics (IJPAM), Vol. 51, No. 1 (2009), pp.33-37.
- S. K. Datta, T. Biswas and MD. A. Hoque.: On some growth properties of differential polynomials in the light of relative order, Italian Journal of Pure and Applied Mathematics, Vol. N 32 (2014), pp. 235-246..
- S. K. Datta, T. Biswas and S. Bhattacharyya : On relative order and relative type based growth properties of differential monomials, Journal of the Indian Math. Soc., Vol. 82, Nos. (3 - 4), (2015), pp. 39–52.
- S. K. Datta, T. Biswas and C. Biswas: Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 8 No. IV (July, 2014), pp. 207-218.
- W. K. Hayman : Meromorphic Functions, The Clarendon Press, Oxford (1964).
- B. K. Lahiri and D. Banerjee : Relative order of entire and meromorphic functions, Proc. Nat. Acad. Sci. India Ser. A., Vol. 69(A), No. 3, (1999), pp.339-354.
- I. Lahiri : Deficiencies of differential polynomials, Indian J. Pure Appl. Math.,Vol.30, No.5(1999), pp.435-447.
- I. Lahiri and S. K. Datta : Growth and value distribution of differential monomials, Indian Journal of Pure and Applied Mathematics, Vol.32, No.12 ( December, 2001), pp.1831-1841.
- L.R. Sons : Deficiencies of monomials, Math.Z, Vol.111(1969), pp.53-68.
- E. C. Titchmarsh : The theory of functions, 2nd edition, Oxford University Press, Oxford, 1939.
- L. Yang : Value distribution theory and new research on it, Science Press, Beijing (1982).
- H. X. Yi : On a result of Singh, Bull. Austral. Math. Soc., Vol. 41(1990), pp.417-420.
- G. Valiron : Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.
Comparative growth measures of differential monomials and differential polynomials depending on their relative orders
Year 2016,
Volume: 4 Issue: 4, 306 - 321, 31.12.2016
Sanjib Kumar Datta
Tanmay Biswas
Debasmita Dutta
Abstract
In the paper we establish some new results depending on the comparative growth properties of composite entire or meromorphic functions using relative order ( relative lower order ) and differential monomials, differential polynomials generated by one of the factors.
References
- L. Bernal : Crecimiento relativo de funciones enteras. Contribución al estudio de lasfunciones enteras con13 ̆053'fndice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
- L. Bernal : Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp.209-229.
- N. Bhattacharjee and I. Lahiri : Growth and value distribution of differential polynomials, Bull. Math. Soc. Sc. Math. Roumanie Tome, Vol. 39(87), No.1-4(1996), pp.85-104.
- W. Bergweiler : On the Nevanlinna characteristic of a composite function, Complex Variables, Vol. 10 (1988), pp. 225-236.
- W. Doeringer : Exceptional values of differential polynomials, Pacific J. Math.,Vol 98, No.1(1982), pp.55-62.
- S. K. Datta : On the order and type of differential monomials, Journal of Pure Mathematics, C.U., Vol.19 (2002), pp.13-17.
- S. K. Datta : On the generalized order and generalized type of differential monomials and differential polynomials, Journal of Mechanics of Continua and Mathematical Sciences, Vol. 2, No. 1 (2007), pp.71-79,
- S. K. Datta and S. Kar : On the growth of differential monomials, International Journal of Pure and Applied Mathematics (IJPAM), Vol. 45, No. 4 (2008), pp.573-585.
- S. K. Datta and S. Kar : Some comparative growth properties of differential polynomials, International Journal of Mathematical Sciences and Engineering Applications (IJMSEA), Vol. 3, No. 1 (2009), pp.113-128.
- S. K. Datta and T. Biswas : On the growth of differential polynomials, Wesleyan Journal of Research, Vol. 2, No. 2 (2009), pp.27-37.
- S. K. Datta and A. R. Das : Some results on the growth properties of differential monomials, International Mathematical Forum, Vol. 4, No. 38 (2009), pp.1863-1876.
- S. K. Datta and E. Jerin : On the growth estimates of differential monomials and differential polynomials generated by meromorphic functions, Journal of Mathematics, N.B.U., Vol. 3 No. 1 (2010), pp.33-52.
- S. K. Datta and A. R. Das : Derivation of some results of maximum terms of differential monomials generated by entire functions, Wesleyan Journal of Research, Vol. 4, No. 1 (2011 ) pp. 15-21.
- S. K. Datta, A. R. Das and A. R. Maji : Maximum terms of differential monomials generated by entire functions, International Journal of Mathematical Sciences and Engineering Applications (IJMSEA), Vol. 5, No. IV (July, 2011), pp.353-359.
- S. K. Datta and A. R. Maji : On different kinds of orders and types of differential monomials generated by transcendental entire functions using their minimum modulus, International Journal of Contemporary Mathematical Sciences, Vol. 6 , No. 42 (2011), pp. 2057 - 2074.
- S. K. Datta and A. R. Maji : On different kinds of orders and types of differential polynomials generated by entire functions using their minimum modulus, International Journal of Mathematical Analysis, Vol. 5, No. 43 (2011), pp. 2127 - 2140.
- S. K. Datta and A. R. Das : Estimation of growth properties of differential polynomials generated by entire functions on the basis of their maximum terms, Review Bulletin of the Calcutta Mathematical Society, Vol. 19, No. 2 (2011), pp. 193-200.
- S. K. Datta and T. Biswas : On a result of Bergweiler, International Journal of Pure and Applied Mathematics (IJPAM), Vol. 51, No. 1 (2009), pp.33-37.
- S. K. Datta, T. Biswas and MD. A. Hoque.: On some growth properties of differential polynomials in the light of relative order, Italian Journal of Pure and Applied Mathematics, Vol. N 32 (2014), pp. 235-246..
- S. K. Datta, T. Biswas and S. Bhattacharyya : On relative order and relative type based growth properties of differential monomials, Journal of the Indian Math. Soc., Vol. 82, Nos. (3 - 4), (2015), pp. 39–52.
- S. K. Datta, T. Biswas and C. Biswas: Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 8 No. IV (July, 2014), pp. 207-218.
- W. K. Hayman : Meromorphic Functions, The Clarendon Press, Oxford (1964).
- B. K. Lahiri and D. Banerjee : Relative order of entire and meromorphic functions, Proc. Nat. Acad. Sci. India Ser. A., Vol. 69(A), No. 3, (1999), pp.339-354.
- I. Lahiri : Deficiencies of differential polynomials, Indian J. Pure Appl. Math.,Vol.30, No.5(1999), pp.435-447.
- I. Lahiri and S. K. Datta : Growth and value distribution of differential monomials, Indian Journal of Pure and Applied Mathematics, Vol.32, No.12 ( December, 2001), pp.1831-1841.
- L.R. Sons : Deficiencies of monomials, Math.Z, Vol.111(1969), pp.53-68.
- E. C. Titchmarsh : The theory of functions, 2nd edition, Oxford University Press, Oxford, 1939.
- L. Yang : Value distribution theory and new research on it, Science Press, Beijing (1982).
- H. X. Yi : On a result of Singh, Bull. Austral. Math. Soc., Vol. 41(1990), pp.417-420.
- G. Valiron : Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.