Starlike Functions of Complex Order with Respect to Symmetric Points Defined Using Higher Order Derivatives

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.

Coefficient Inequalities of a Comprehensive Subclass of Analytic Functions With Respect to Symmetric Points

“…We can easily see that the function has a normalization ψ(0) = 1, Re [ψ(ξ)] > 0 and maps unit disc on to the cardioid with cusp on the left hand side (also see Karthikeyan et al [24]).…”

“…In Figure 1, we have shown that an ellipsoidlike region (see 1(a)) becomes a cardioid with cusp on the right hand side on the impact of Janowski function. The impact of Janowski function on various conic region has been studied by Karthikeyan et al [24]. The function 1 + tanh ξ has a Maclaurin series of the form…”

Properties of Meromorphic Spiral-Like Functions Associated with Symmetric Functions

“…The purpose to study Δ τ σ ðξÞ was mainly motivated by the study of Karthikeyan et al [10] and Noor and Malik [11]. Here, we will list some recent studies.…”

Classes of Multivalent Spirallike Functions Associated with Symmetric Regions

“…Remark 3. In [12], Karthikeyan et al have showed that convex function becomes starlike by varying the parameters in ∆ λ 0 (z). Hence, the function ∆ λ σ (z) may be convex univalent or starlike univalent depending on the function χ(z).…”