Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
harmonic univalent starlike functions; Dziok-Srivastava operator; distortion bounds; extreme points; uniformly convex functions
harmonic univalent starlike functions; Dziok-Srivastava operator; distortion bounds; extreme points; uniformly convex functions
Summary:
Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.
References:
[1] Avici, Y., Zlotkiewicz, E.: On harmonic univalent mappings. Ann. Univ. Mariae Curie-Skłodowska Sect. A 44 (1990), 1–7. MR 1157872
[2] Carlson, B. C., Shaffer, B.: Starlike and prestarlike hypergeometric functions. SIAM J. Math. Anal. 15 (2002), 737 – 745. DOI 10.1137/0515057 | MR 0747433
[3] Clunie, J., Sheil-Small, T.: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Math. 9 (1984), 3–25. MR 0752388 | Zbl 0506.30007
[4] Dziok, J., Srivastava, H. M.: Certain subclasses of analytic functions associated with the generalized hypergeometric function. Integral Transform. Spec. Funct. 14 (2003), 7–18. DOI 10.1080/10652460304543 | MR 1949212 | Zbl 1040.30003
[5] Goodman, A. W.: On uniformly convex functions. Ann. Polon. Math. 1991 (56), 87–92. MR 1145573
[6] Jahangiri, J. M., Silverman, H.: Harmonic univalent functions with varying rrguments. Int. J. Appl. Math. 8 (3) (2002), 267–275. MR 1898507
[7] Murugusundaramoorthy, G.: A class of Ruscheweyh-Type harmonic univalent functions with varying arguments. Southwest J. Pure Appl. Math. 2 (2003), 90–95. MR 2052983 | Zbl 1050.30010
[8] Rønning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc. 118 (1993), 189–196. MR 1128729
[9] Rosy, T., Stephen, B. A., Subramanian, K. G., Jahangiri, J. M.: Goodman-Ronning type harmonic univalent functions. Kyungpook Math. J. 41 (2001), 45–54. MR 1847436 | Zbl 0988.30012
[10] Ruscheweyh, S.: New criteria for univalent functions. Proc. Amer. Math. Soc. 49 (1975), 109–115. DOI 10.1090/S0002-9939-1975-0367176-1 | MR 0367176 | Zbl 0303.30006
[11] Ruscheweyh, S.: Neighborhoods of univalent functions. Proc. Amer. Math. Soc. 81 (1981), 521–528. DOI 10.1090/S0002-9939-1981-0601721-6 | MR 0601721 | Zbl 0458.30008
[12] Srivastava, H. M., Owa, S.: Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators and certain subclasses of analytic functions. Nagoya Math. J. 106 (1998), 1–28. MR 0894409
[13] Vijaya, K.: Studies on certain subclasses of harmonic functions. Ph.D. thesis, VIT University, 2006.
Search
Partner of
