Sains Malaysiana 41(12)(2012): 1657–1661

 

An Operator Defined by Convolution Involving the

Generalised Hurwitz-Lerch Zeta Function

(Pengoperasi yang Ditakrif oleh Konvolusi MelibatkanPengitlakan Fungsi Hurwitz-Lerch Zeta)

 

 

Aabed Mohammed & Maslina Darus*

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D. Ehsan, Malaysia

 

Diserahkan: 18 Mei 2012 / Diterima: 14 Ogos 2012

 

ABSTRACT

In this article, we studied the generalised Hurwitz-Lerch zeta function. We defined a new operator and introduced a new class of function. Here, some interesting properties and sufficient conditions for subordination were also studied.

 

Keywords: Hadamard product; Hurwitz-Lerch zeta function; integral operator

 

ABSTRAK

Dalam kertas kerja ini, fungsi teritlak Hurwitz–Lerch zeta dikaji. Pengoperasi baharu dan kelas fungsi baharu diperkenalkan. Di sini beberapa sifat dan syarat cukup untuk subordinasi juga dikaji.

 

Kata kunci: Fungsi Hurwitz-LCerch zeta; hasil darab Hadamard; pengoperasi kamiran

RUJUKAN

Ajwely, A. & Darus, M. 2011. On the Fekete-Szego theorem for the generalized Owa-Srivastava operator. Proceedings of the Romanian Academy Series A 12: 179-188.

Al-Abbadi, M.H. & Darus, M. 2011. The Fekete-Szego theorem for a certain class of analytic functions. Sains Malaysiana40: 385-389.

Al-Shaqsi, K. & Darus, M. 2008. An operator defined by convolution involving the polylogarithms functions. Journal of Mathematics and Statistics 4: 46-50.

Bernardi, S.D. 1969. Convex and starlike univalent functions. Transaction American Mathematical Society 135: 429-446.

Darus, M. & Faisal, I. 2010. Hankel determinant for the class of K (α, β). Journal of Quality Measurement and Analysis 6(2): 77-85.

Eenigenburg, P., Miller, S.S., Mocanu, P.T. & Reade, M.O. 1983. On a Briot-Bouquet differential subordination, in General Inequalities, vol. 64 of Internationale Schriftenreihe zur Numerischen Mathematik. pp. 339-348, Basel, Switzerland. Birkhauser.

Goyal, S.P. & Laddha, R.K. 1997. On the generalized Riemann zeta functions and the generalized Lambert transform. Ganita Sandesh11: 99-108.

Kanemitsu, S., Katsurada, M. &Yoshimoto, M. 2000. On the Hurwitz-Lerch zeta-function. Aequationes Mathematics 59: 1-19.

Lin, S. & Srivastava, H.M. 2004. Some families of the Hurwitz-Lerch zeta functions and associated fractional derivative and other integral representations. Applied Mathematics and Computation 154: 725-733.

Noor, K.I. 1999. On new classes of integral operators. Journal of Natural Geometry 16: 71-80.

Noor, K.I. & Noor, M.A. 1999. On integral operators. Journal of Mathematical Analysis and Applications 238: 341-352.

Padmanabhan, K.S. & Parvatham, R. 1985. Some applications of differential subordination. Bulletin of the Australian Mathematical Society 33: 321-330.

Ruscheweyh, St. 1975. New criteria for univalent functions. Proceedings of American Mathematcal Society 49: 109-115.

Salagean, G.S. 1983. Subclasses of univalent functions. Lecture Notes in Math. 1013: 262-372.

*Pengarang surat-menyurat; e-mail: maslina@ukm.my

 

 

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