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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 25 โ€ข Issue 4 โ€ข PP: 346-356 โ€ข 2025

Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function

Jamal Salah 1*
1College of Applied and Health Sciences, A'Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman
* Corresponding Author.
Received: November 07, 2024 Revised: December 28, 2024 Accepted: January 24, 2025

Abstract

This study, aims to consider the coefficients of the reciprocal Gamma function in order introduce a linear operator by the means of Hadamard product. Thus, we define a new subclass of uniformly starlike functions of order ๐›ผ, Γ−1(๐›ผ). Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions ๐‘“∈Γ−1(๐›ผ). In addition, we investigate the inclusion conditions for the Hadamard product and the Integral transform.

Keywords

Uniformly starlike functions Gamma function reciprocal Gamma function Hadamard product

References

[1] J. M. Borwein and R. M. Corless, "Gamma and factorial in the monthly," Amer. Math. Monthly, vol. 125, no. 5, pp. 400–424, 2018.

[2] P. J. Davis, "Leonhard Euler’s integral: A historical profile of the gamma function: In memoriam: Milton Abramowitz," Amer. Math. Monthly, vol. 66, no. 10, pp. 849–869, 1959.

[3] J. Y. Salah, "A note on gamma function," Int. J. Modern Sci. Eng. Technol. (IJMSET), vol. 2, no. 8, pp. 58–64, 2015.

[4] J. W. Jr. Wrench, "Concerning two series for the gamma function," Math. Compute, vol. 22, pp. 617–626, 1968.

[5] L. Fekih-Ahmed, "On the power series expansion of the reciprocal gamma function," 2014, [Online]. Available: hal-01029331v1.

[6] A. W. Goodman, "On uniformly convex functions," Ann. Polon. Math., vol. 56, pp. 87–92, 1991.

[7] A. W. Goodman, "On uniformly starlike functions," J. Math. Anal. Appl., vol. 155, pp. 364–370, 1991.

[8] W. Ma and D. Minda, "Convex functions," Ann. Polon. Math., pp. 165–175, 1992.

[9] G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990.

[10] F. H. Jackson, "On q-definite integrals," Quart. J. Pure Appl. Math., vol. 41, pp. 193–203, 1910.

[11] G. Murugusundaramoorthy and N. Magesh, "Linear operators associated with a subclass of uniformly convex functions," IJPAMS, vol. 3, no. 1, pp. 113–125, 2006.

[12] B. A. Frasin, "On certain subclasses of analytic functions associated with Poisson distribution series," Acta Univ. Sapientiae, Mathematica, vol. 11, no. 1, pp. 78–86, 2019.

[13] R. Shah and A. Kumar, "Subclasses of analytic functions associated with generalized Pascal distribution," Math. Methods Appl. Sci., vol. 44, no. 12, pp. 9530–9546, 2021, doi: 10.1002/mma.7345.

[14] A. Ali and M. Hossain, "Investigation of starlike and convex functions associated with modified Pascal distribution series," Complex Anal. Oper. Theory, vol. 17, no. 2, pp. 155–170, 2023, doi: 10.1007/s11785-023-01432-w.

[15] A. Amourah, B. Frasin, and G. Murugusundaramoorthy, "On certain subclasses of uniformly spirallike functions associated with struve functions," J. Math. Comput. Sci., vol. 11, pp. 4586–4598, 2021.

[16] S. M. El-Deeb and G. Murugusundaramoorthy, "Applications on a subclass of β-uniformly starlike functions connected with q-Borel distribution," Asian-European J. Math., vol. 2250158, 2023.

[17] J. Salah, H. U. Rehman, I. Al Buwaiqi, A. Al Azab, and M. Al Hashmi, "Subclasses of spiral-like functions associated with the modified Caputo's derivative operator," AIMS Math., vol. 8, no. 8, pp. 18474–18490, 2023, doi: 10.3934/math.2023939.

 

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Salah, Jamal. "Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, 2025, pp. 346-356. DOI: https://doi.org/10.54216/IJNS.250429
Salah, J. (2025). Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function. International Journal of Neutrosophic Science, Volume 25(Issue 4), 346-356. DOI: https://doi.org/10.54216/IJNS.250429
Salah, Jamal. "Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function." International Journal of Neutrosophic Science Volume 25, no. Issue 4 (2025): 346-356. DOI: https://doi.org/10.54216/IJNS.250429
Salah, J. (2025) 'Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function', International Journal of Neutrosophic Science, Volume 25(Issue 4), pp. 346-356. DOI: https://doi.org/10.54216/IJNS.250429
Salah J. Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 4):346-356. DOI: https://doi.org/10.54216/IJNS.250429
J. Salah, "Subclass of uniformly starlike functions associated with a linear operator whose coefficients are the reciprocal Gamma function," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, pp. 346-356, 2025. DOI: https://doi.org/10.54216/IJNS.250429
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