Majorization problems for two subclasses of analytic functions connected with the Liu–Owa integral operator and exponential function

Abstract

In the present paper, we investigate majorization properties for the class of uniformly starlike functions and the class of spiral-like functions related to an exponential function, which are defined through the Liu–Owa integral operator given by (1.5). Also, some special cases of our main results in a form of corollaries are shown.

Majorization for Certain Classes of Analytic Functions Defined by Fournier–Ruscheweyh Integral Operator

“…A majorization problem for the normalized class of starlike functions has been investigated by MacGregor [1] and further studied by Altintas et al [14]. Recently, a number of researchers have studied several majorization problems for univalent and multivalent functions or meromorphic and multivalent meromorphic functions involving different operators and different classes [14][15][16][17][18][19][20][22][23][24]. By motivating the above work, the majorization problems of the classes S a k [M, N, μ], R a k(μ), and T a k(θ) are investigated 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].…”

Majorization problems for certain starlike functions associated with the exponential function

“…Indeed, he has been studied majorization problem for the class of starlike functions [16]. Recently, also many researchers have studied several majorization problems for certain subclasses of analytic functions which are defined by the concept of subordination, see for instance [1,2,25,22,23,24]. The present paper aims to study majorization problems for the classes S * e and S * B without acting upon any linear or nonlinear operators to the above function classes.…”