Subclass of Analytic Functions Defined by Miller-Ross-Type Poisson Distribution Series

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DOI: https://doi.org/10.28924/2291-8639-23-2025-60
Published: Mar 3, 2025
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Chandrasekharan Nataraj, Mukil Alagirisamy, H. Niranjan, P. Thirupathi Reddy, B. Venkateswarlu, Subclass of Analytic Functions Defined by Miller-Ross-Type Poisson Distribution Series, Int. J. Anal. Appl., 23 (2025), 60.

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Chandrasekharan Nataraj, Mukil Alagirisamy, H. Niranjan, P. Thirupathi Reddy, B. Venkateswarlu

Abstract

It is very well-known that the special functions and integral operators play a vital role in the research of applied and mathematical sciences. The main purpose of this paper is to introduce a new subclass of analytic functions involving Miller-Ross functions and obtain coefficient inequalities, distortion theorem, convex linear combination, partial sums, convolution, and neighborhood results for this class.

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References

  1. S. Altinkaya, S. Yalin, Poisson Distribution Series for Certain Subclasses of Starlike Functions With Negative Coefficients, Anal. Univ. Orad Fasc. Mat. 24 (2017), 5-8.
  2. D. Bajpai, A Study of Univalent Functions Associated With Distortion Series and q-Calculus, Thesis, CSJM Univerity, Kanpur, India, (2016).
  3. L. Brickman, D.J. Hallenbeck, T.H. Macgregor, D.R. Wilken, Convex Hulls and Extreme Points of Families of Starlike and Convex Mappings, Trans. Amer. Math. Soc. 185 (1973), 413–413. https://doi.org/10.1090/S0002-9947-1973-0338337-5.
  4. M. Caglar, H. Orhan, On Neighborhood and Partial Sums Problem for Generalized Sakaguchi Type Functions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 63 (2017), 17-28.
  5. M. Çaglar, E. Deniz, Partial Sums of the Normalized Lommel Functions, Math. Inequal. Appl. 18 (2015), 1189–1199. https://doi.org/10.7153/mia-18-92.
  6. E. Deniz, H. Orhan, Some Properties of Certain Subclasses of Analytic Functions with Negative Coefficients by Using Generalized Ruscheweyh Derivative Operator, Czech. Math. J. 60 (2010), 699–713. https://doi.org/10.1007/s10587-010-0064-9.
  7. E. Deniz, H. Orhan, Certain Subclasses of Multivalent Functions Defined by New Multiplier Transformations, Arabian J. Sci. Eng. 36 (2011), 1091–1112. https://doi.org/10.1007/s13369-011-0103-3.
  8. S.M. El-Deeb, T. Bulboaca, J. Dziok, Pascal Distribution Series Connected with Certain Subclasses of Univalent Functions, Kyungpook Math. J. 59 (2019), 301–314. https://doi.org/10.5666/KMJ.2019.59.2.301.
  9. Sheza.M. El-Deeb, G. Murugusundaramoorthy, A. Alburaikan, Bi-Bazileviˇc Functions Based on the Mittag-LefflerType Borel Distribution Associated with Legendre Polynomials, J. Math. Comput. Sci. 24 (2021), 235–245. https://doi.org/10.22436/jmcs.024.03.05.
  10. B.A. Frasin, Generalization of Partial Sums of Certain Analytic and Univalent Functions, Appl. Math. Lett. 21 (2008), 735–741. https://doi.org/10.1016/j.aml.2007.08.002.
  11. B.A. Frasin, S. Porwal, F. Yousef, Subclasses of Starlike and Convex Functions Associated with Mittag-Leffler-type Poisson Distribution Series, Montes Taurus J. Pure Appl. Math. 3 (2021), 147–154.
  12. B.A. Frasin, Subclass of Analytic Functions with Negative Coefficients Related with Miller-Ross-Type Poisson Distribution Series, Acta Univ. Sapientiae, Math. 15 (2023), 109–122. https://doi.org/10.2478/ausm-2023-0007.
  13. B.A. Frasin, L.I. Cotirla, On Miller–Ross-Type Poisson Distribution Series, Mathematics 11 (2023), 3989. https://doi.org/10.3390/math11183989.
  14. A.W. Goodman, Univalent Functions and Nonanalytic Curves, Proc. Amer. Math. Soc. 8 (1957), 598–601. https://doi.org/10.1090/S0002-9939-1957-0086879-9.
  15. Q. Hu, T.G. Shaba, J. Younis, et al. Applications of q -Derivative Operator to Subclasses of Bi-Univalent Functions Involving Gegenbauer Polynomials, Appl. Math. Sci. Eng. 30 (2022), 501–520. https://doi.org/10.1080/27690911.2022.2088743.
  16. S. Kazimoglu, E. Deniz, M. Caglar, Partial Sums of the Bessel-Struve Kernel Function, in: 3rd International Conference on Mathematical and Related Sciences: Current Trend and Developments, pp. 267-275, 2020.
  17. S. Kazımo ˘glu, Partial Sums of The Miller-Ross Function, Turk. J. Sci. 6 (2021), 167-173.
  18. L. Jian-Lin, S. Owa, On Partial Sums of the Libera Integral Operator, J. Math. Anal. Appl. 213 (1997), 444–454. https://doi.org/10.1006/jmaa.1997.5549.
  19. K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, 1993.
  20. G. Murugusundaramoorthy, S.M. El-Deeb, Second Hankel Determinant for a Class of Analytic Functions of the Mittag-Leffler-Type Borel Distribution Related With Legendre Polynomials, TWMS J. Appl. Eng. Math. 12 (2022), 1247-1258.
  21. G. Murugusundaramoorthy, H.Ö. Güney, D. Breaz, Starlike Functions of the Miller–Ross-Type Poisson Distribution in the Janowski Domain, Mathematics 12 (2024), 795. https://doi.org/10.3390/math12060795.
  22. W. Nazeer, Q. Mehmood, S.M. Kang, A. Ul Haq, An Application of Binomial Distribution Series on Certain Analytic Functions, J. Comput. Anal. Appl. 26 (2019), 11-17.
  23. H. Orhan, N. Yagmur, Partial Sums of Generalized Bessel Functions, J. Math. Inequal. 4 (2014), 863–877. https://doi.org/10.7153/jmi-08-65.
  24. S. Owa, H.M. Srivastava, N. Saito, Partial Sums of Certain Classes of Analytic Functions, Int. J. Comput. Math. 81 (2004), 1239–1256. https://doi.org/10.1080/00207160412331284042.
  25. S. Porwal, M. Kumar, A Unified Study on Starlike and Convex Functions Associated with Poisson Distribution Series, Afr. Mat. 27 (2016), 1021–1027. https://doi.org/10.1007/s13370-016-0398-z.
  26. S. Porwal, K.K. Dixit, On Mittag-Leffler Type Poisson Distribution, Afr. Mat. 28 (2017), 29–34. https://doi.org/10.1007/s13370-016-0427-y.
  27. V. Ravichandran, Geometric Properties of Partial Sums of Univalent Functions, Math. Newslett. 22 (2012), 208-221.
  28. M.S. Ur Rehman, Q.Z. Ahmad, H.M. Srivastava, B. Khan, N. Khan, Partial Sums of Generalized q-Mittag-Leffler Functions, AIMS Math. 5 (2020), 408–420. https://doi.org/10.3934/math.2020028.
  29. S. Ruscheweyh, Neighborhoods of Univalent Functions, Proc. Amer. Math. Soc. 81 (1981), 521–521. https://doi.org/10.1090/S0002-9939-1981-0601721-6.
  30. B. ¸Seker, S. Suuml;mer Eker, B. Cekic, On Subclasses of Analytic Functions Associated with Miller-Ross-Type Poisson Distribution Series, Sahand Commun. Math. Anal. 19 (2022), 69-79. https://doi.org/10.22130/scma.2022.551474.1091.
  31. B. SEKER, S. SUMER EKER, B. CEKIC, Certain Subclasses of Analytic Functions Associated With Miller-Ross-Type Poisson Distribution Series, Honam Math. J. 44 (2022), 504–512. https://doi.org/10.5831/HMJ.2022.44.4.504.
  32. T. Sheil-Small, A Note on the Partial Sums of Convex Schlicht Functions, Bull. Lond. Math. Soc. 2 (1970), 165–168. https://doi.org/10.1112/blms/2.2.165.
  33. L. Shi, B. Ahmad, N. Khan, et al. Coefficient Estimates for a Subclass of Meromorphic Multivalent Q-Close-toConvex Functions, Symmetry 13 (2021), 1840. https://doi.org/10.3390/sym13101840.
  34. H. Silverman, Univalent Functions with Negative Coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116. https://doi.org/10.1090/S0002-9939-1975-0369678-0.
  35. H. Silverman, Partial Sums of Starlike and Convex Functions, J. Math. Anal. Appl. 209 (1997), 221–227. https://doi.org/10.1006/jmaa.1997.5361.
  36. E.M. Silvia, Partial Sums of Convex Functions of Order α , Houston J. Math. 11 (1985), 397–404.
  37. H.M. Srivastava, S. Gaboury, F. Ghanim, Partial Sums of Certain Classes of Meromorphic Functions Related to the Hurwitz-Lerch Zeta Function, Moroccan J. Pure Appl. Anal. 1 (2015), 38–50. https://doi.org/10.7603/s40956-015-0003-8.
  38. H.M. Srivastava, G. Murugusundaramoorthy, S.M. El-Deeb, Faber Polynomial Coefficient Estimates of Bi-Closeto-Convex Functions Connected with the Borel Distribution of the Mittag-Leffler Type, J. Nonlinear Var. Anal. 5 (2021), 103–118. https://doi.org/10.23952/jnva.5.2021.1.07.
  39. H.M. Srivastava, S.M. El-Deeb, Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution, Symmetry 13 (2021), 1023. https://doi.org/10.3390/sym13061023.
  40. H.M. Srivastava, B. Seker, S.S. Eker, B. Cekic, A Class of Poisson Distributions Based Upon a Two Parameter Mittag-Leffler Type Function, J. Nonlinear Convex Anal. 24 (2023), 475-485.
  41. S. Sümer Eker, S. Ece, Geometric Properties of the Miller-Ross Functions, Iran. J. Sci. Technol. Trans. A: Sci. 46 (2022), 631–636. https://doi.org/10.1007/s40995-022-01268-8.
  42. G. Sujatha, K.K. Viswanathan, B. Venkateswarlu, H. Niranjan, P.T. Reddy, Certain Subclass of Analytic Functions Defined By q-Analogue Differential Operator, Math. Stat. 12 (2024), 465–474. https://doi.org/10.13189/ms.2024.120508.
  43. B. Venkateswarlu, P.T. Reddy, G. Sujatha, S. Sridevi, On a Certain Subclass of Analytic Functions Involving Pascal Distribution Series, Bull. Comput. Appl. Math. 1 (2022), 145-165.
  44. N. Yagmur, H. Orhan, Partial Sums of Generalized Struve Functions, Miskolc Math. Notes 17 (2016), 657-670. https://doi.org/10.18514/MMN.2016.1419.
  45. C. Zhang, B. Khan, T.G. Shaba, J.-S. Ro, S. Araci, M.G. Khan, Applications of Q-Hermite Polynomials to Subclasses of Analytic and Bi-Univalent Functions, Fractal Fract. 6 (2022), 420. https://doi.org/10.3390/fractalfract6080420.