Making use of fractional q-calculus operators, we introduce a new subclass ℳq(λ,γ,k) of starlike functions and determine the coefficient estimate, extreme points, closure theorem, and distortion bounds for functions in ℳq(λ,γ,k). Furthermore we discuss neighborhood results, subordination theorem, partial sums, and integral means inequalities for functions in ℳq(λ,γ,k).

In this paper we obtain certain results on multivalent functions, as an application of the principle of subordination, with fixed second coefficient. The influence of the second coefficient of p-valent functions is realized in the results obtained.

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Abstract. Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.

In this paper, we introduce new subclasses of convex and starlike functions with respect to other points. The coefficient estimates for these classes are obtained. ReThese functions are called starlike with respect to symmetric points and were introduced by Sakaguchi in 1959. Ashwah and Thomas in [2] introduced another class namely the class S * c consisting of functions starlike with respect to conjugate points.