Geodesic
Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series
Mathematica Bohemica, Tome 147 (2022) no. 3, pp. 407-417
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes $\mathcal {SP}_{p}(\alpha ,\beta )$ and $\mathcal {UCV}_{p}(\alpha ,\beta )$ of uniformly spirallike functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.
The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes $\mathcal {SP}_{p}(\alpha ,\beta )$ and $\mathcal {UCV}_{p}(\alpha ,\beta )$ of uniformly spirallike functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.
DOI : 10.21136/MB.2021.0132-20
Classification : 30C45
Keywords: analytic function; Hadamard product; uniformly spirallike function; Pascal distribution series 
@article{10_21136_MB_2021_0132_20,
     author = {Murugusundaramoorthy, Gangadharan and Frasin, Basem Aref and Al-Hawary, Tariq},
     title = {Uniformly convex spiral functions and uniformly spirallike functions associated with {Pascal} distribution series},
     journal = {Mathematica Bohemica},
     pages = {407--417},
     year = {2022},
     volume = {147},
     number = {3},
     doi = {10.21136/MB.2021.0132-20},
     mrnumber = {4482314},
     zbl = {07584133},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0132-20/}
}
TY  - JOUR
AU  - Murugusundaramoorthy, Gangadharan
AU  - Frasin, Basem Aref
AU  - Al-Hawary, Tariq
TI  - Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series
JO  - Mathematica Bohemica
PY  - 2022
SP  - 407
EP  - 417
VL  - 147
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0132-20/
DO  - 10.21136/MB.2021.0132-20
LA  - en
ID  - 10_21136_MB_2021_0132_20
ER  - 
%0 Journal Article
%A Murugusundaramoorthy, Gangadharan
%A Frasin, Basem Aref
%A Al-Hawary, Tariq
%T Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series
%J Mathematica Bohemica
%D 2022
%P 407-417
%V 147
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0132-20/
%R 10.21136/MB.2021.0132-20
%G en
%F 10_21136_MB_2021_0132_20
Murugusundaramoorthy, Gangadharan; Frasin, Basem Aref; Al-Hawary, Tariq. Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series. Mathematica Bohemica, Tome 147 (2022) no. 3, pp. 407-417. doi: 10.21136/MB.2021.0132-20

[1] Al-Hawary, T., Frasin, B. A.: Uniformly analytic functions with varying arguments. An. Univ. Oradea, Fasc. Mat. 23 (2016), 37-44. | MR | JFM

[2] Cho, N. E., Woo, S. Y., Owa, S.: Uniform convexity properties for hypergeometric functions. Fract. Calc. Appl. Anal. 5 (2002), 303-313. | MR | JFM

[3] Dixit, K. K., Pal, S. K.: On a class of univalent functions related to complex order. Indian J. Pure Appl. Math. 26 (1995), 889-896. | MR | JFM

[4] El-Ashwah, R. M., Kota, W. Y.: Some condition on a Poisson distribution series to be in subclasses of univalent functions. Acta Univ. Apulensis, Math. Inform. 51 (2017), 89-103. | DOI | MR | JFM

[5] El-Deeb, S. M., Bulboacă, T.: Differential sandwich-type results for symmetric functions connected with a $q$-analog integral operator. Mathematics 7 (2019), 17 pages, Article ID 1185. | DOI

[6] El-Deeb, S. M., Bulboacă, T., Dziok, J.: Pascal distribution series connected with certain subclasses of univalent functions. Kyungpook Math. J. 59 (2019), 301-314. | DOI | MR | JFM

[7] Frasin, B. A.: Comprehensive family of uniformly analytic functions. Tamkang J. Math. 36 (2005), 243-254. | DOI | MR | JFM

[8] Frasin, B. A.: Quasi-Hadamard product of certain classes of uniformly analytic functions. Gen. Math. 16 (2008), 29-35. | MR | JFM

[9] Frasin, B. A.: On certain subclasses of analytic functions associated with Poisson distribution series. Acta Univ. Sapientiae, Math. 11 (2019), 78-86. | DOI | MR | JFM

[10] Frasin, B. A.: Two subclasses of analytic functions associated with Poisson distribution. Turkish J. Ineq. 4 (2020), 25-30.

[11] Frasin, B. A., Aldawish, I.: On subclasses of uniformly spiral-like functions associated with generalized Bessel functions. J. Funct. Spaces 2019 (2019), Article ID 1329462, 6 pages. | DOI | MR | JFM

[12] Frasin, B. A., Al-Hawary, T., Yousef, F.: Necessary and sufficient conditions for hypergeometric functions to be in a subclass of analytic functions. Afr. Mat. 30 (2019), 223-230. | DOI | MR | JFM

[13] Frasin, B. A., Aydoğan, S. M.: Pascal distribution series for subclasses of analytic functions associated with conic domains. Afr. Mat. 32 (2021), 105-113. | DOI | MR | JFM

[14] Frasin, B. A., Gharaibeh, M. M.: Subclass of analytic functions associated with Poisson distribution series. Afr. Mat. 31 (2020), 1167-1173. | DOI | MR | JFM

[15] Goodman, A. W.: On uniformly convex functions. Ann. Pol. Math. 56 (1991), 87-92. | DOI | MR | JFM

[16] Goodman, A. W.: On uniformly starlike functions. J. Math. Anal. Appl. 155 (1991), 364-370. | DOI | MR | JFM

[17] Kanas, S., Wiśniowska, A.: Conic regions and $k$-uniform convexity. J. Comput. Appl. Math. 105 (1999), 327-336. | DOI | MR | JFM

[18] Kanas, S., Wiśniowska, A.: Conic domains and starlike functions. Rev. Roum. Math. Pures Appl. 45 (2000), 647-657. | MR | JFM

[19] Merkes, E. P., Scott, W. T.: Starlike hypergeometric functions. Proc. Am. Math. Soc. 12 (1961), 885-888. | DOI | MR | JFM

[20] Murugusundaramoorthy, G.: Subclasses of starlike and convex functions involving Poisson distribution series. Afr. Mat. 28 (2017), 1357-1366. | DOI | MR | JFM

[21] Murugusundaramoorthy, G., Vijaya, K., Porwal, S.: Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series. Hacet. J. Math. Stat. 45 (2016), 1101-1107. | DOI | MR | JFM

[22] Porwal, S.: Mapping properties of generalized Bessel functions on some subclasses of univalent functions. An. Univ. Oradea, Fasc. Mat. 20 (2013), 51-60. | MR | JFM

[23] Porwal, S.: An application of a Poisson distribution series on certain analytic functions. J. Complex Anal. 2014 (2014), Article ID 984135, 3 pages. | DOI | MR | JFM

[24] Porwal, S., Kumar, M.: A unified study on starlike and convex functions associated with Poisson distribution series. Afr. Mat. 27 (2016), 1021-1027. | DOI | MR | JFM

[25] Ravichandran, V., Selvaraj, C., Rajagopal, R.: On uniformly convex spiral functions and uniformly spirallike functions. Soochow J. Math. 29 (2003), 392-405. | MR | JFM

[26] nning, F. Rø: On starlike functions associated with parabolic regions. Ann. Univ. Mariae Curie-Skłodowska, Sect. A 45 (1991), 117-122. | MR | JFM

[27] nning, F. Rø: Uniformly convex functions and a corresponding class of starlike functions. Proc. Am. Math. Soc. 118 (1993), 189-196. | DOI | MR | JFM

[28] Selvaraj, C., Geetha, R.: On subclasses of uniformly convex spirallike functions and corresponding class of spirallike functions. Int. J. Contemp. Math. Sci. 5 (2010), 1845-1854. | MR | JFM

[29] Silverman, H.: Starlike and convexity properties for hypergeometric functions. J. Math. Anal. Appl. 172 (1993), 574-581. | DOI | MR | JFM

[30] Srivastava, H. M., Murugusundaramoorthy, G., Sivasubramanian, S.: Hypergeometric functions in the parabolic starlike and uniformly convex domains. Integral Transforms Spec. Funct. 18 (2007), 511-520. | DOI | MR | JFM

Cité par Sources :