Subclasses of Starlike Functions Associated with Fractional q-Calculus Operators

Certain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...

Certain Subclasses of Multivalent Functions Associated with Fractional Calculus Operator

By means of the generalized fractional calculus operator, we introduce and investigate a subclass of p−valent functions with negative coefficients. We obtain the coefficient estimates, distortion bounds for the class. Furthermore, we discuss inclusion relationship involving the neighborhood result of the same. Mathematics Subject Classification: 30C45

q-ANALOGUES OF SAIGO’S FRACTIONAL CALCULUS OPERATORS

M. Saigo [Math. Rep. Coll. Gen. Educ., Kyushu Univ., 11 (1978) 135-143] has defined a pair of fractional integral operators and fractional derivatives involving generalizd hypergeometric function. The aim of present paper is to define their q-analogues. First, we define a pair of q-analogues of Saigo’s fractional integral operators and establish some results for it. Next, we define a pair of q-...

Inequalities Defining Certain Subclasses of Analytic and Multivalent Functions Involving Fractional Calculus Operators

Making use of a certain fractional calculus operator, we introduce two new subclasses Mδ(p;λ, μ, η) and Tδ(p;λ, μ, η) of analytic and p−valent functions in the open unit disk. The results investigated exhibit the sufficiency conditions for a function to belong to each of these classes. Several geometric properties of such multivalent functions follow, and these consequences are also mentioned.

On Some Subclasses of Harmonic Functions Defined by Fractional Calculus