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Datta, Sanjib Kumar
- On Relative Order and Relative Type Based Growth Properties of Differential Monomials
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Authors
Affiliations
1 Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, 741235, West Bengal, IN
2 Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia, 741101, West Bengal, IN
3 Jhorehat F. C. High School for Girls, P.O.- Jhorehat, Dist-Howrah, 711302, West Bengal, IN
1 Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, 741235, West Bengal, IN
2 Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia, 741101, West Bengal, IN
3 Jhorehat F. C. High School for Girls, P.O.- Jhorehat, Dist-Howrah, 711302, West Bengal, IN
Source
The Journal of the Indian Mathematical Society, Vol 82, No 3-4 (2015), Pagination: 39-52Abstract
In this paper some newly developed results based on the growth properties of relative order (relative lower order), relative type (relative lower type) and relative weak type of differential monomials generated by entire and meromorphic functions are investigated.Keywords
Entire Function, Meromorphic Function, Relative Order, Relative Type, Differential Monomial.
- On Different Relative Growth Factors of Entire Functions
Abstract Views :293 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, University of Kalyani, Kalyani, IN
2 Department of Mathematics, Darjeeling Government College, Darjeeling, IN
3 Department of Mathematics, Chakdaha College, Chakdaha, IN
1 Department of Mathematics, University of Kalyani, Kalyani, IN
2 Department of Mathematics, Darjeeling Government College, Darjeeling, IN
3 Department of Mathematics, Chakdaha College, Chakdaha, IN
Source
The Journal of the Indian Mathematical Society, Vol 87, No 1-2 (2020), Pagination: 37–55Abstract
In this paper we investigate some properties related to sum and product of different relative growth factors of an entire function with respect to another entire function in connection with a special type of non-decreasing, unbounded function ψ.Keywords
Entire function, Growth, Order (Lower Order), (p;q;t)L−ψ-order (p;q;t)L−ψ−Lower Order), Non-Decreasing, Unbounded Function.References
- R. P. Agarwal, S. K. Datta, T. Biswas and P. Sahoo, On the growth analysis of iterated entire functions, Advanced Studies in Contemporary Mathematics. 26(1) (2016) , 93-137.
- L. Bernal, Orden relativ de crecimiento de funciones enteras, Collect Mth. 39(1988), 209-229.
- T. Biswas, Some results relating to sum and product theorems of relative (p,q, t)L-th order and relative (p,q, t)L-th type of entire functions, Korean J. Math. 26(2) (2018), 215-269.
- S. K. Datta, T. Biswas and C. Ghosh, On relative (p,q)-th order based growth measure of entire functions, Filomat. 30 (7) (2016) , 1723-1735.
- W. K. Hayman, Meromorphic functions, The Calendron Press, Oxford, 1964.
- 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.
- 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.
- L. M. Sanchez Ruiz, S. K. Datta, T. Biswas, and G. K. Mandal, On the (p,q)th relative order and oriented growth properties of entire functions, Abstr. Appl. Anal. 2014, Article ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
- D. Somasundaram, and R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J. Pure. Appl. Math. 19 (3)(1988), 284-293.
- H. M. Srivastava, S. K. Datta, T. Biswas and D. Dutta, Sum and product theorems depending on the (p,q)-th order and (p,q)-th type of entire functions, Cogent Mathematics. 2015, 2 : 1107951, 1-22.
- T. Samten and N. Biswas, Some results on the integer translation of composite entire and meromorphic functions, Konuralp J. Math. 5(2) (2017), 1-11.
- G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.
- Linear Differential Equations with Solutions of Finite Iterated p-Φ Order
Abstract Views :135 |
PDF Views:2
Authors
Affiliations
1 Department of Mathematics, Kazi Nazrul University, Asansol-713340, IN
2 Department of Mathematics, University of Kalyani, Kalyani - 741235, IN
3 53, Gopalpur Primary School, Raninagar-I, Murshidabad -742304, IN
4 28, Dolua Dakshinpara Haridas Primary School, Beldanga, Murshidabad -742133, IN
1 Department of Mathematics, Kazi Nazrul University, Asansol-713340, IN
2 Department of Mathematics, University of Kalyani, Kalyani - 741235, IN
3 53, Gopalpur Primary School, Raninagar-I, Murshidabad -742304, IN
4 28, Dolua Dakshinpara Haridas Primary School, Beldanga, Murshidabad -742133, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 1-2 (2023), Pagination: 23-36Abstract
In this article, we have studied complex linear homogeneous differential equations whose coefficients are entire functions having finite iterated p − Φ order and the growth of its nontrivial solutions.Keywords
Entire Function, Iterated p − Φ Order, Finiteness Degree.References
- L. G. Bernal, On growth k−order of solutions of a complex homogeneous linear differential equation, Proc. Amer. Math. Soc., 101 (2)(1987), 317–322.
- I. Chyzhykov, J. Heittokangas and J. R¨atty¨a, Finiteness of φ-order of solutions of linear differential equations in the unit disc, J. Anal. Math., 109 (2009), 163–198.
- W. K. Hayman, Meromorphic Functions. Oxford Mathematical Monographs Clarendon Press, Oxford, 1964.
- H. Herold, Differentialgleichungen im Komplexen, Vandenhoeck & Ruprecht, G¨ottingen, 1975.
- G. Jank and L. Volkman, Meromorphe Funktionen Und Differentialgleichungen, Birk¨auser, Basel-Boston, 1985.
- L. Kinnunen, Linear differential equations with solutions of finite iterated order, South-east Asian Bull. Math., 22 (4)(1998), 385–405.
- I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, New Work, 1993.
- D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), 411–414.
- M. N. Seremetao, On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Izv. Vyssh. Uchebn. Zaved. Mat., 2 (1967), 100–108.
- X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q] − φ order, Advances in Difference Equations 2014, 2014:200.