Majorization and Coefficient Problems for a General Class of Starlike Functions

Abstract

In the current paper, we study a majorization issue for a general category S * ( ϑ ) of starlike functions, the region of which is often symmetric with respect to the real axis. For various special symmetric functions ϑ , corresponding consequences of the main result are also presented with some relevant connections of the outcomes rendered here with those obtained in recent research. Moreover, coefficient bounds for some majorized functions are estimated.

Majorization Results for Certain Subfamilies of Analytic Functions

“…Numerous articles have been published in which this idea was used. The work of Altintas and Srivastava [5], Cho et al [6], Goswami and Aouf [7], Goyal and Goswami [8,9], Li et al [10], Panigraht and El-Ashwah [11], Prajapat and Aouf [12], and the authors [13,14] are worth mentioning on this topic.…”

New Results for Some Generalizations of Starlike and Convex Functions

“…Lemma 4 (see [19], Theorem 2). If g ∈ A, f ∈ S * ðφÞ with g ðzÞ ≪ f ðzÞ, then jg′ðzÞj ≤ j f ′ðzÞj for all z in the disk | z | ≤r1, where r1 is the smallest positive root of the equation…”

“…3 Journal of Function Spaces Cho et al [19] studied the majorization issue for the category S * ðφÞ of starlike functions as follows:…”

Majorization Properties for Certain Subclasses of Meromorphic Function of Complex Order

“…Majorization ( 12) is closely related to the concept of quasi-subordination between analytic functions in U. Several researchers have published articles on this topic; for example, Tang et al [12] gave the concept of majorization for subclasses of starlike functions based on the sine and cosine functions, Arif et al [13] discussed majorization for various new defned classes, Cho et al [14] obtained coefcient estimates for majorization, and Tang and Deng [15] defned the majorization problem connected with Liu-Owa integral operator and exponential function. Tis concept is also defned for p− valent function by Altintas and Srivastava [16] and for complex order by Altintas et al [17].…”