Abstract
In this article, we introduce and investigate a novel class of analytic functions that are defined through a second-order differential inequality in conjunction with the error function, a fundamental mathematical function widely used in various scientific and engineering applications. The proposed class of functions provides a versatile framework for modeling complex phenomena in diverse fields, including mathematics, physics, engineering, and statistics. And we examine coefficient bound, extreme points, convolution, convexity and radii properties of this subclass. In summary, our investigation into this class of analytic functions, defined by a second-order differential inequality and the error function, not only contributes to the mathematical literature but also provides a powerful tool for solving complex problems in science and engineering. The versatility and potential applications of these functions make them a valuable resource for researchers and practitioners seeking innovative solutions to diverse analytical challenges.
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References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Dorer Publications Inc., New York (1965)
Alzer, H.: Error functions inequalities. Adv. Comput. Math. 33, 349–379 (2010)
Coman, D.: The radius of starlikeness for error function. Stud. Univ. Babeş-Bolyai Math. 36, 13–16 (1991)
Elbert, A., Laforgia, A.: The zeros of the complementary error function. Numer. Algorithms 49, 153–157 (2008)
Sayedain Boroujeni, S.H., Najafzadeh, S.: Error function and certain subclasses of analytic univalent functions. Sahand Commun. Math. Anal. 20(1), 107–117 (2023). https://doi.org/10.22130/scma.2022.556794.1136
Ramachandran, C., Vanitha, L., Kanas, S.: Certain results on qstarlike and q-convex error functions. Math. Slovaca 68, 361–368 (2018)
Gao, C.-Y., Zhou, S.-Q.: Certain subclass of starlike functions. Appl. Math. Comput. 187, 176–182 (2007)
Bernardi, S.D.: Convex and starlike univalent functions. Trans. Am. Math. Soc. 135, 429–446 (1969)
Libera, R.J.: Some classes of regular univalent functions. Proc. Am. Math. Soc. 16, 755–758 (1965)
Livingston, A.E.: On the radius of univalence of certain analytic functions. Proc. Am. Math. Soc. 17, 352–357 (1966)
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Nas, M., Yalçın, S. & Bayram, H. A Class of Analytic Functions Defined by a Second Order Differential Inequality and Error Function. Int. J. Appl. Comput. Math 10, 42 (2024). https://doi.org/10.1007/s40819-024-01681-0
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DOI: https://doi.org/10.1007/s40819-024-01681-0