Geometric properties of normalized imaginary error function
DOI:
https://doi.org/10.24193/subbmath.2022.2.19Keywords:
Univalent function, close-to-convex, error function, imaginary error function.Abstract
The error function takes place in a wide range in the fields of mathematics, mathematical physics and natural sciences. The aim of the current paper is to investigate certain properties such as univalence and close-to-convexity of normalized imaginary error function, which its region is symmetric with respect to the real axis. Some other outcomes are also obtained.
Mathematics Subject Classification (2010): 30C45, 30C50, 33B20.
Received 27 August 2021; Accepted 27 August 2021.
References
Abramowitz, M., Stegun, I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications Inc., New York, 1965.
Adegani, E.A., Bulboaca, T., New properties of the generalized Dini function, Hacet. J. Math. Stat., 49(2020), no. 5, 1753-1760.
Alzer, H., Error function inequalities, Adv. Comput. Math., 33(2010), no. 3, 349-379.
Aouf, M.K., Mostafa, A.O., Zayed, H.M., Sufficiency conditions for hypergeometric functions to be in a subclasses of analytic functions, Kyungpook Math. J., 56(2016), 235-248.
Aouf, M.K., Mostafa, A.O., Zayed, H.M., Necessity and sufficiency for hypergeometric functions to be in a subclass of analytic functions, J. Egyptian Math. Soc., 23(2015), 476-481.
Bansal, D., Sokol, J., Geometric properties of Mathieu-type power series inside unit disk, J. Math. Inequal., 13(2019), no. 4, 911-918.
Bansal, D., Soni, M.K., Soni, A., Certain geometric properties of the modified Dini function, Anal. Math. Phys., 9(2019), 1383-1392.
Baricz, A., Deniz, E., Yagmur, N., Close-to-convexity of normalized Dini functions, Math. Nachr., 289(2016), 1721-1726.
Baricz, A., Toklu, E., Kadioglu, E., Radii of starlikeness and convexity of Wright functions, Math. Commun., 23(2018), no. 1, 97-117.
Chaudhry, M.A., Qadir, A., Zubair, S.M., Generalized error functions with applications to probability and heat conduction, Int. J. Appl. Math., 9(2002), 259-278.
Coman, D., The radius of starlikeness for the error function, Stud. Univ. Babes-Bolyai Math., 36(1991), no. 2, 13-16.
Elbert, A., Laforgia, A., The zeros of the complementary error function, Numer. Algorithms, 49(2008), 153-157.
Fej´er, L., Untersuchungen u¨ber Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Acta Literarum Sci., 8(1936), 89-115.
Fettis, H.E., Caslin, J.C., Cramer, K.R., Complex zeros of the error function and of the complementary error function, Math. Comp., 27(1973), 401-407.
Herden, G., The role of error-functions in order to obtain relatively optimal classification, In: Classification and Related Methods of Data Analysis (Aachen, 1987), North-Holland, Amsterdam, 1988, 105-111.
Noreen, S., Raza, M., Liu, J.L., Arif, M., Geometric properties of normalized Mittag-Leffler functions, Symmetry, 11(2019), no. 1, Article ID 45, 1-13.
Ozaki, S., On the theory of multivalent functions, Sci. Rep. Tokyo Bunrika Daigaku A, 2(1935), 167-188.
Prajapat, J.K., Certain geometric properties of the Wright functions, Integral Transforms Spec. Funct., 26(2015), no. 3, 203-212.
Raducanu, D., Geometric properties of Mittag-Leffler functions, In: Models and Theories in Social Systems, Springer, Berlin, Germany, 2019, 403-415.
Ramachandran, C., Vanitha, L., Kanas, S., Certain results on q-starlike and q-convex error functions, Math. Slovaca, 68(2018), no. 2, 361-368.
Ruscheweyh, St., Convolutions in Geometric Function Theory, Presses Univ. Montr´eal, Montreal, 1982.
Sahoo, S.K., Sharma, N.L., On a generalization of close-to-convex functions, Ann. Polon. Math., 113(2015), no. 1, 93-108.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.