On some applications of relative $(p,q)$-th order for rating the growths of composite entire functions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 3-25.

Voir la notice de l'article provenant de la source Math-Net.Ru

The main aim of this paper is to study some comparative growth properties of composite entire functions on the basis of relative $(p,q)$-th order and relative $(p,q)$-th lower order of entire function with respect to another entire function where $p$ and $q$ are any two positive integers.
@article{BASM_2023_3_a0,
     author = {Tanmay Biswas},
     title = {On some applications of relative $(p,q)$-th order for rating the growths of composite entire functions},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--25},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2023_3_a0/}
}
TY  - JOUR
AU  - Tanmay Biswas
TI  - On some applications of relative $(p,q)$-th order for rating the growths of composite entire functions
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2023
SP  - 3
EP  - 25
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2023_3_a0/
LA  - en
ID  - BASM_2023_3_a0
ER  - 
%0 Journal Article
%A Tanmay Biswas
%T On some applications of relative $(p,q)$-th order for rating the growths of composite entire functions
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2023
%P 3-25
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2023_3_a0/
%G en
%F BASM_2023_3_a0
Tanmay Biswas. On some applications of relative $(p,q)$-th order for rating the growths of composite entire functions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 3-25. http://geodesic.mathdoc.fr/item/BASM_2023_3_a0/

[1] Bernal-Gonzaléz L., Crecimiento relativo de funciones enteras, Aportaciones al estudio de las funciones enteras con índice exponencial finito, Doctoral Thesis, Universidad de Sevilla, Spain, 1984

[2] Bernal L., “Orden relative de crecimiento de funciones enteras”, Collect. Math., 39 (1988), 209–229 | MR | Zbl

[3] Biswas T., “On some inequalities concerning relative $(p$,$q)$-$ \varphi $ type and relative $(p$,$q)$-$\varphi $ weak type of entire or meromorphic functions with respect to an entire function”, J. Class. Anal., 13:2 (2018), 107–122 | DOI | MR | Zbl

[4] Biswas T., “Growth analysis of composite entire functions from the view point of relative $(p,q)$-th order”, Korean J. Math., 26:3 (2018), 405–425 | DOI | MR

[5] Biswas T., “A note on some growth properties of composite entire and meromorphic functions using their relative $(p,q)$-th orders”, Electron J. Math. Anal. Appl., 7:2 (2019), 151–167 | MR | Zbl

[6] Biswas T., “Further study on the results of Sheremeta”, Commun. Fac. Sci. Univ. Ank. Se. A1. Math. Stat., 68:1 (2019), 1007–1018 | DOI | MR | Zbl

[7] Biswas T., “Measures of comparative growth analysis of composite entire functions on the basis of their relative $(p,q)$-th type and relative $(p,q)$-th weak type”, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 26:1 (2019), 13–33 | DOI | MR | Zbl

[8] Clunie J., “The composition of entire and meromorphic functions”, Mathematical Essays dedicated to A. J. Macintyre, Ohio University Press, 1970, 75–92 | MR

[9] Datta S. K., Biswas T., “Growth of entire functions based on relative order”, Int. J. Pure Appl. Math., 51:1 (2009), 49–58 | MR | Zbl

[10] Datta S. K., Biswas T., “Relative order of composite entire functions and some related growth properties”, Bull. Cal. Math. Soc., 102:3 (2010), 259–266 | MR | Zbl

[11] Datta S. K., Biswas T., Biswas R., “Comparative growth properties of composite entire functions in the light of their relative order”, Math. Student, 82:1-4 (2013), 209–216 | MR

[12] Datta S. K., Maji A. R., “Relative order of entire functions in terms of their maximum terms”, Int. Journal of Math. Analysis, 5:43 (2011), 2119–2126 | MR | Zbl

[13] Juneja O. P., Kapoor G. P., 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 | MR | Zbl

[14] Lahiri B. K., Banerjee D., “Relative fix points of entire functions”, J. India Acad. Math., 19:1 (1997), 87–97 | MR | Zbl

[15] Lahiri B. K., Banerjee D., “Entire functions of relative order $(p,q)$”, Soochow J. Math., 31:4 (2005), 497–513 | MR | Zbl

[16] Ruiz L. M. S. , Datta S. K., Biswas T., Mondal G. K., “On the $ (p,q)$-th relative order oriented growth properties of entire functions”, Abstr. Appl. Anal., 2014, 86137, 8 pp. | DOI | MR

[17] Sato D., “On the rate of growth of entire functions of fast growth”, Bull. Amer. Math. Soc., 69 (1963), 411–414 | DOI | MR | Zbl

[18] Singh A. P., “On maximum term of composition of entire functions”, Proc. Nat. Acad. Sci. India, 59(A), Part I (1989), 103–115 | MR | Zbl

[19] Singh A. P., Baloria M. S., “On the maximum modulus and maximum term of composition of entire functions”, Indian J. Pure Appl. Math., 22:12 (1991), 1019–1026 | MR | Zbl

[20] Shen. X., Tu J., Xu H. Y., “Complex oscillation of a second-order linear differential equation with entire coefficients of $[p$,$ q]$-$\varphi $ order”, Adv. Difference Equ., 200:2014 (2014), 14 http://www.advancesindifferenceequations.com/content/2014/1/200 | MR | Zbl

[21] Titchmarsh E. C., The theory of functions, 2nd ed., Oxford University Press, Oxford, 1968 | MR

[22] Valiron G., Lectures on the general theory of integral functions, Chelsea Publishing Company, New York, 1949 | MR