Glasnik Matematicki, Vol. 37, No.1 (2002), 59-71.

ON CERTAIN SUBCLASSES OF p-VALENT FUNCTIONS DEFINED IN TERMS OF CERTAIN FRACTIONAL DERIVATIVE OPERATORS

R. K. Raina and T. S. Nahar

Department of Mathematics, Govt. Postgraduate College, Bhilwara - 311001, Rajasthan, India

Abstract.   In the present paper we study certain subclasses H_λ,μ,η(a,b,pσ) and K_λ,μ,η(a,b,pσ) of analytic and p-valent functions. The results presented include coefficient estimates and distorsion properties for functions belonging to such classes. Further results giving closure theorems, various properties and modified Hadamard products of several functions belonging to above classes are also mentioned.

2000 Mathematics Subject Classification.   26A33, 30C45.

Key words and phrases.   Analytic and p-valent functions, fractional derivative operator, Riemann-Liouville and Erdelyi-Kober operators, Hadamard products.