Geodesic
On a subclass of analytic functions defined by Bell distribution series
Lagad, A.1 ; Ingle, R. N. 2 ; Reddy, P. T. 3
1 Department of Mathematics, N.E.S. Science College, Nanded-431 605, Maharashtra, India
2 Department of Mathematics, Bahirji Smarak Mahavidyalay, Bashmathnagar-431 512, Hingoli Dist., Maharashtra, India
3 Department of Mathematics, DRK Institute of Science and Technology, Bowrampet, Hyderabad-500 043, Telangana, India
Journal of nonlinear sciences and its applications, Tome 18 (2025) no. 1, p. 33-42.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The Bell distribution is a major and helpful model that may be applied to a wide variety of real-world situations and problems. Bell distributions play a significant role in geometric function theory, particularly in the study of univalent functions and their properties. The importance of Bell distributions in geometric function theory lies in their ability to provide a combinatorial framework for analyzing the properties and behaviors of univalent functions. By leveraging these distributions, mathematicians can gain deeper insights into the geometric and analytic aspects of complex functions, enhancing both theoretical understanding and practical applications. The main purpose of this paper is to introduce a new subclass of analytic functions involving Bell distribution series and obtain coefficient inequalities, distortion theorem, convex linear combination, convolution and neighborhood result for this class.
DOI : 10.22436/jnsa.018.01.04
Classification : 30C45, 30C50
Keywords: Analytic, starlike, convexity, coefficient estimate, neighborhood

Lagad, A. 1 ; Ingle, R. N.  2 ; Reddy, P. T.  3

1 Department of Mathematics, N.E.S. Science College, Nanded-431 605, Maharashtra, India
2 Department of Mathematics, Bahirji Smarak Mahavidyalay, Bashmathnagar-431 512, Hingoli Dist., Maharashtra, India
3 Department of Mathematics, DRK Institute of Science and Technology, Bowrampet, Hyderabad-500 043, Telangana, India 
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Lagad, A.; Ingle, R. N. ; Reddy, P. T. . On a subclass of analytic functions defined by Bell distribution series. Journal of nonlinear sciences and its applications, Tome 18 (2025) no. 1, p. 33-42. doi : 10.22436/jnsa.018.01.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.018.01.04/

[1] Amourah, A.; Alomari, M.; Yousef, F.; Alsoboh, A. Consolidation of a Certain Discrete Probability Distribution with a Subclass of Bi-Univalent Functions Involving Gegenbauer Polynomials, Math. Probl. Eng., Volume 2022 (2022), pp. 1-6 | DOI

[2] Amourah, A.; Frasin, B. A.; Ahmad, M.; Yousef, F. Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions, Symmetry, Volume 14 (2022), pp. 1-8 | DOI

[3] Amourah, A.; Al-Hawary, T.; Yousef, F.; Salah, J. Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials, Int. J. Neutrosophic Sci. (IJNS), Volume 25 (2025), pp. 228-238

[4] Bain, L.; Engelhardt, M. Introduction to Probability and Mathematical Statistics, Duxburry Press:, Belmont, CA, USA, 1992

[5] Bell, E. T. Exponential polynomials, Ann. of Math. (2), Volume 35 (1934), pp. 258-277 | Zbl | DOI

[6] Bell, E. T. Exponential numbers, Amer. Math. Monthly, Volume 41 (1934), pp. 411-419 | DOI

[7] Castellares, F.; Ferrari, S. L. P.; Lemonte, A. J. On the Bell distribution and its associated regression model for count data, Appl. Math. Model., Volume 56 (2018), pp. 172-185 | Zbl | DOI

[8] Darwish, H. E.; Lashin, A. Y.; Hassan, B. F. Neighborhood properties of generalized Bessel function, Glob. J. Sci. Front. Res., Volume 15 (2015), pp. 21-26

[9] Goodman, A. W. Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., Volume 8 (1957), pp. 598-601 | DOI

[10] Goodman, A. W. On uniformly convex functions, Ann. Polon. Math., Volume 56 (1991), pp. 87-92 | DOI

[11] Hu, Q.; Shaba, T. G.; Younis, J.; Khan, B.; Mashwani, W. K.; glar, M. Ça˘ Applications of q-derivative operator to subclasses of bi-univalent functions involving Gegenbauer polynomials, Appl. Math. Sci. Eng., Volume 30 (2022), pp. 501-520 | DOI

[12] Kanas, S.; Wisniowska, A. Conic regions and k-uniform convexity, J. Comput. Appl. Math., Volume 105 (1999), pp. 327-336 | Zbl | DOI

[13] glu, S. Kazimo˘ Neighborhoods of certain classes of analytic functions defined by Miller-Ross function, Cauc. J. Sci., Volume 8 (2021), pp. 165-172 | DOI

[14] Littlewood, J. E. On Inequalities in the Theory of Functions, Proc. London Math. Soc. (2), Volume 23 (1925), pp. 481-519 | DOI

[15] Murugusundaramoorthy, G. A unified class of analytic functions with negative coefficients involving the Hurwitz-Lerch zeta function, Bull. Math. Anal. Appl., Volume 1 (2009), pp. 71-84 | Zbl

[16] Murugusundaramoorthy, G.; Vijaya, K.; Uma, K. Subordination results for a class of analytic functions involving the Hurwitz-Lerch zeta function, Int. J. Nonlinear Sci., Volume 10 (2010), pp. 430-437 | Zbl

[17] Rønning, F. Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., Volume 118 (1993), pp. 189-196 | DOI | Zbl

[18] Rønning, F. On uniform starlikeness and related Properties of univalent functions, Complex Variables Theory Appl., Volume 24 (1994), pp. 233-239 | Zbl | DOI

[19] Ruschweyh, S. Neighborhoods of univalent functions, Proc. Amer. Math. Soc., Volume 81 (1981), pp. 521-527 | DOI

[20] Shi, L.; Ahmad, B.; Khan, N.; Khan, M. G.; Araci, S.; Mashwani, W. K.; Khan, B. Coefficient estimates for a subclass of meromorphic multivalent -close-to-convex functions, Symmetry, Volume 13 (2021), pp. 1-12 | DOI

[21] Silverman, H. Univalent functions with negative coefficients, Proc. Amer. Math. Soc., Volume 51 (1975), pp. 109-116 | DOI

[22] Silverman, H. A survey with open problems on univalent functions whose coefficients are negative, Rocky Mountain J. Math., Volume 21 (1991), pp. 1099-1125 | DOI | Zbl

[23] Silverman, H. Integral means for univalent function with negative coefficients, Houston J. Math., Volume 23 (1997), pp. 169-174 | Zbl

[24] Reddy, P. Thirupathi; Venkateswarlu, B. A certain subclass of uniformly convex functions defined by Bessel functions, Proyecciones, Volume 38 (2019), pp. 719-731 | Zbl

[25] Zhang, C.; Khan, B.; Shaba, T. G.; Ro, J.-S.; Araci, S.; Khan, M. G. Applications of q- Hermite Polynomials to subclasses of analytic and Bi-Univalent functions, Fractal Fract., Volume 6 (2022), pp. 1-15 | DOI

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