Generalized k–uniformly convex harmonic functions with negative coefficients

Shuhai Li, Huo Tang, Lina Ma, Ao En

Abstract


In the present paper, we introduce some generalized $k$-uniformly convex harmonic functions with negative coefficients. Sufficient coefficient conditions, distortion bounds, extreme points, Hadamard product and partial sum for functions of these classes are obtained.

Keywords


Harmonic functions; k–uniformly convex; extreme points; distortion bounds

Full Text:

PDF

References


P. L. Duren. Univalent Functions. Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.

J. Clunie and T. Sheil Small. Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 39(1984), 3--25.

J. M. Jahangiri, Coefficient bounds and univalent criteria for harmonic functions with negative coefficients, Ann. Univ. Marie-Curie Sklodowska Sect. A, 52(1998), 57--66.

J. M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal. Appl., 235(1999), 470--477.

H. Silverman, Harmonic univalent function with negative coefficients, J. Math. Anal. Appl., 220(1998), 283--289.

H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math., 28(1999), 275--284.

M. Ozturk, S. Yalcin and M. Yamankaradeniz, Convex subclass of harmonic starlike functions, Appl. Math. Comput., 154(2004),449--459.

S. Nagpal and V. Ravichandran, A comprehensive class of harmonic functions defined by convolution and its connection with integral transforms and hypergeometric functions, Stud. Univ. Babes-Bolyai Math., 59(2014), 41--55.

A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1991), 87--92.

F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1993), 189--196.

Ma. W. C and D. Minda, Uniformly convex functions}, Ann. Polon. Math., 57(1992), 165--175.

F. Ronning, On starlike functions associated with parabolic regions, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 45(1991), 117--122.

S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105(1999), 327--336.

S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transforms Spec. Funct., 9(2000), 121--132.

W. C. Ma nad D. Minda, A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Tianjin,1992, 157--169, Conf. Proc. Lecture Notes Anal. I, Int. Press, Cambridge, MA, 1994.

Shuhai Li, Huo Tang, Lina Ma and En Ao, A new class of harmonic multivalent meromorphic functions, Bull. Math. Anal. Appl., 7(2015), 20--30.

R. M. El-Ashwah and B. A. Frasin, Hadamard product of certain harmonic univalent meromorphic functions, Theory and Applications of Mathematics Computer Science, 5(2015), 126--131.

H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl., 209(1997), 221--227.

E. M. Silvia, On partial sums of convex functions of order alpha, Houston J. Math., 11(1985), 397--404.

S. Porwal, Partial sums of certain harmonic univalent function, Lobachevskii J. Math., 32(2011), 366--375.

S. Porwal and K. K. Dixit, Partial sums of starlike harmonic univalent function, Kunpook Math. J., 50(2010), 433--445.

S. Porwal, A convolution approach on partial sums of certain harmonic univalent function}, Internat. J. Math. Math. Sci., 2012, Art. ID 509349, 1--12.




DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.2326

Sponsored by Tamkang University | ISSN 0049-2930 (Print), ISSN 2073-9826 (Online) | Powered by MathJax