Abstract
Problem statement: By means of the Hadamard product (or convolution), new class of function of power order was formed. This class was motivated by many authors namely MacGregor, Umezawa, Darus and Ibrahim and many others. The class indeed extended in the form of integral operator due to the work of Bernardi, Libera and Li vingston. Approach: A new class of multivalent analytic functions in the open unit disk U was intr oduced. An application of this class was posed by using the fractional integral operator. The integra l operator of multivalent functions was proposed an d defined. The previous well known integral operator was mentioned. Results: Having the integral operator, a class was defined and coefficient bound s established by using standard method. These results reduced to well-known results studied by va rious authors. The operator was then applied for fractional calculus and obtained the coefficient bo unds. Conclusion: Therefore, new operators could be obtained with some earlier results and standard methods. New classes were formed and new results of special cases were obtained.
Highlights
Let Σp, α denote the class of functions of the form: which are analytic in the unit disk U
N=2 which are analytic in the unit disk U: = {z∈C, |z|
The previous operators will be mentioned to highlight the importance of simple operator which can be extended to a complicated ones and yet interesting to study
Summary
Let Σp, α denote the class of functions of the form: which are analytic in the unit disk U. For the Hadamard product or convolution of two power series f defined in (2) and a function g where: ∑ ∞. F (z) = zp+α + anzn+p+α ,(0 ≤ α < 1) (1). N=2 which are analytic in the unit disk U: = {z∈C, |z|
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