Abstract
Problem statement: We introduced a new bijective convolution linear operator defined on the class of normalized analytic functions. This operator was motivated by many researchers namely Srivastava, Owa, Ruscheweyh and many others. The operator was essential to obtain new classes of analytic functions. Approach: Simple technique of Ruscheweyh was used in our preliminary approach to create new bijective convolution linear operator. The preliminary concept of Hadamard products was mentioned and the concept of subordination was given to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. In fact, the subordinating factor sequence was used to derive different types of subordination results. Results: Having the linear operator, subordination theorems were established by using standard concept of subordination. The results reduced to well-known results studied by various researchers. Coefficient bounds and inclusion properties, growth and closure theorems for some subclasses were also obtained. Conclusion: Therefore, many interesting results could be obtained and some applications could be gathered.
Highlights
Let A denote the class of functions f normalized by: ∑ ∞f (z) = z + a nzn+1 (1)n =1 which are analytic in the open unit disk U = {z :| z |< 1}, let T denote the subclass of A consisting of functions of the form: ∑∞f (z) = z − anzn+1, n =1We denote by K the class of functions f ∈ A that are convex in U : Using the convolution techniques, Ruscheweyh[1] introduced and studied the class of prestarlike functions of order β
N =1 which are analytic in the open unit disk U = {z :| z |< 1}, let T denote the subclass of A consisting of functions of the form:
Coefficient bounds and Inclusions: we investigate sufficient conditions for the function f ∈ A to be in the classes S(m,λ,a, b,α) and C(m,λ,a, b,α) by obtaining the coefficient bounds
Summary
Let A denote the class of functions f normalized by: ∑ ∞. N =1 which are analytic in the open unit disk U = {z :| z |< 1} , let T denote the subclass of A consisting of functions of the form: ∑∞. F (z) = z − anzn+1, (an ≥ 0, z ∈ U) n =1. We denote by K the class of functions f ∈ A that are convex in U : Using the convolution techniques, Ruscheweyh[1] introduced and studied the class of prestarlike functions of order β. F∈ A is said to be prestarlike function of order β (0 ≤ β < 1) if f (z) * sβ (z) is starlike function of order β, where: ∑ sβ(z) = z (1 − z)2(1−β)
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