On a certain class of harmonic functions and the generalized Bernardi-Libera-Livingston integral operator
DOI:
https://doi.org/10.24193/subbmath.2020.3.05Keywords:
Harmonic univalent functions, extreme points, varying arguments, Hadamard product, integral operator.Abstract
In this paper we examine the closure properties of the class VH(F ; γ) under the generalized Bernardi-Libera-Livingston integral operator Lc(f ), (c > −1) which is defined by Lc(f ) = Lc(h) + Lc(g), f = h + g, h and g are analytic functions, where Lc(h)(z) = z c + 1 r zc 0 (tc−1 h(t)dt and Lc(g)(z) = z c + 1 r zc 0 (tc−1 g(t)dt. The obtained results are sharp and they improve known results.
Mathematics Subject Classification (2010): 30C45, 30C50.
References
Al-Kharsani, H.A., Al-Khai, R.A., Univalent harmonic functions, J. Inequal. Pure Appl. Math., 8(2007), no. 2, Art. 59, 8 pp.
Carlson, B.C., Shaffer, S.B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15(1984), no. 4, 737-745.
Clunie, J., Sheil-Small, T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A.I. Math., 9(1984), 3-25.
Jahangiri, J.M., Murugusundaramoorthy, G., Vijaya, K., S˘al˘agean-type harmonic univalent functions, Southwest J. Pure Apll. Math., (2002), no. 2, 77-82.
Jahangiri, J.M., Murugusundaramoorthy, G., Vijaya, K., Starlikeness of harmonic functions defined by Ruscheweyh derivatives J. Indian Acad. Math., 26(2004), no. 1, 191-200.
Jahangiri, J.M., Silverman, H., Harmonic univalent functions with varying arguments, Int. J. Appl. Math., 8(2002), no. 3, 267-275.
Murugusundaramoorthy, G., A class of Ruscheweyh-type harmonic univalent functions with varying arguments, Southwest J. Pure Appl. Math., 2(2003), 90-95.
Murugusundaramoorthy, G., S˘ala˘gean, G.S., On a certain class of harmonic functions associated with a convolution structure, Mathematica, 54(77)(2012), Special Issue, 131- 142.
Murugusundaramoorthy, G., Vijaya, K., A subclass of harmonic functions associated with Wright hypergeometric functions, Adv. Stud. Contemp. Math. (Kyungshang), 18(2009), no. 1, 87-95.
Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115.
S˘al˘agean, G.S., Subclasses of univalent functions, Complex Analysis, Fifth Romanian- Finnish Seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983.
Srivastava, H.M., Owa, S., Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear opera- tors and certain subclasses of analytic functions, Nagoya Math. J., 106(1987), 1-28.
Wright, E.M., The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc., 46(1940), no. 2, 389-408.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
