A unified class of \(k\)-uniformly convex functions defined by the Dziok-Srivastava linear operator. (English) Zbl 1152.30015
Summary: The main purpose of this paper is to introduce a new class \(\mathcal U\mathcal H(q,s,\lambda,\beta,k)\) of functions which are analytic in the open unit disk \(\Delta={z: z\in\mathbb C\text{ and }|z|<1}\). We obtain various results including a characterization, coefficient estimates, and distortion and covering theorems for functions belonging to the class \(\mathcal U\mathcal H(q,s,\lambda,\beta,k)\).
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
Keywords:
Analytic functions; starlike functions; convex functions; \(k\)-uniformly convex functions; convolution products; Dziok-Srivastava linear operatorReferences:
| [1] | Altintaş, O., On a subclass of certain starlike functions with negative coefficients, Math. Japon., 36, 1-7 (1991) · Zbl 0739.30011 |
| [2] | Aqlan, E.; Jahangiri, J. M.; Kulkarni, S. R., New classes of \(k\)-uniformly convex and starlike functions, Tamkang J. Math., 35, 261-266 (2004) · Zbl 1066.30009 |
| [3] | Dziok, J.; Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103, 1-13 (1999) · Zbl 0937.30010 |
| [4] | Dziok, J.; Srivastava, H. M., Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function, Adv. Stud. Contemp. Math., 5, 115-125 (2002) · Zbl 1038.30009 |
| [5] | Dziok, J.; Srivastava, H. M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct., 14, 7-18 (2003) · Zbl 1040.30003 |
| [6] | Gangadharan, A.; Shanmugam, T. N.; Srivastava, H. M., Generalized hypergeometric functions associated with \(k\)-uniformly convex functions, Comput. Math. Appl., 44, 1515-1526 (2002) · Zbl 1036.33003 |
| [7] | Owa, S.; Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39, 1057-1077 (1987) · Zbl 0611.33007 |
| [8] | Shanmugam, T. N.; Sivasubramanian, S.; Kamali, M., On the unified class of \(k\)-uniformly convex functions associated with Sălăgean derivative, J. Approx. Theory Appl., 1, 141-145 (2005) |
| [9] | Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51, 109-116 (1975) · Zbl 0311.30007 |
| [10] | Srivastava, H. M., Some families of fractional derivative and other linear operators associated with analytic, univalent, and multivalent functions, (Analysis and Its Applications (Chennai, 2000) (2001), Allied Publishers Limited: Allied Publishers Limited New Delhi, Mumbai, Calcutta and Chennai), 209-243 · Zbl 1006.30012 |
| [11] | Srivastava, H. M.; Owa, S.; Chatterjea, S. K., A note on certain classes of starlike functions, Rend. Sem. Mat. Univ. Padova, 77, 115-124 (1987) · Zbl 0596.30018 |
| [12] | Srivastava, H. M.; Saigo, M.; Owa, S., A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl., 131, 412-420 (1988) · Zbl 0628.30014 |
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