Abstract
In this article, we introduce a new class of multivalent analytic functions associated with petal-shape region. Furthermore, some useful properties, such as the Fekete–Szegö inequality, and their consequences for some special cases are discussed. For some specific value of function f, we obtain sufficient conditions for multivalent starlike functions connected with petal-shape domain. Finally, in the concluding section, we draw the attention of the interested readers toward the prospect of studying the basic or quantum (or q-) generalizations of the results, which are presented in this paper. However, the (p,q)-variations of the suggested q-results will provide a relatively minor and inconsequential development because the additional (rather forced-in) parameter p is obviously redundant.
Highlights
Introduction and MotivationTo understand our main results and the notations used in this paper in a better way, some basic literature of Geometric Function Theory is presented here
Motivated by the above-mentioned work, we introduce a new class of analytic multivalent starlike functions associated with the petal-shape domain
For some specific value of function g, we obtain sufficient conditions for multivalent starlike functions connected with the petal-shape domain
Summary
Introduction and MotivationTo understand our main results and the notations used in this paper in a better way, some basic literature of Geometric Function Theory is presented here. Let B0 be the class of Schwarz regular functions w such that w : D → D with property that w(0) = 0 and has power series expansion w(z) = ∑ cnzn. We briefly discuss the notion of subordinations; let Λ1, Λ2 ∈ A, Λ1, is said to subordinate to Λ2 symbolically: Λ1 ≺ Λ2 if there exists an analytic function w(z) with properties that w(0) = 0 and |w(z)| < 1, such that Many authors have studied the subclasses of multivalent (p-valent) functions from different viewpoints and perspectives.
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