Abstract
In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.
Highlights
Introduction and DefinitionsThroughout this paper, we let C, Z− and N to denote the sets of complex numbers, negative integers and natural numbers, respectively
Let H( a, n) be the class comprising of all analytic functions defined in unit disc E = {z ∈ C : |z| < 1} and having a power series representation of the form h(z) = a + an zn + an+1 zn+1 + · · ·
Two prominent subclasses of A are the so-called families of starlike functions and convex functions which have the analytic characterization of the form zh0 (z)
Summary
Throughout this paper, we let C, Z− and N to denote the sets of complex numbers, negative integers and natural numbers, respectively. Let H( a, n) be the class comprising of all analytic functions defined in unit disc E = {z ∈ C : |z| < 1} and having a power series representation of the form h(z) = a + an zn + an+1 zn+1 + · · ·. Let A( p, n) denote the class of functions h analytic in E and having a power series representation of the form h(z) = z p +. Two prominent subclasses of A are the so-called families of starlike functions and convex functions which have the analytic characterization of the form zh0 (z)
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