3 research outputs found
Properties of close-to-convex functions and special functions / Jonathan Aaron Azlan Mosiun
No full textLet S be the class of functions of the form f(z) = z + 1P n=2 anzn that are univalent and analytic in the unit disc U = fz 2 C : jzj < 1g. Study on functions derived via geometric properties such as S_, C and K, which are subclasses of S, has been ongoing for many
decades and has been done extensively and exhaustively. Among the many subclasses
of K, Sakaguchi introduced the class of starlike functions with respect to symmetric
point, denoted by S_
s . Since its introduction in 1959, many authors have introduced
generalizations of S_
s or classes resembling it. Inspired by this, Gao & Zhou introduced
another subclass of K which was denoted as Ks which was further generalized by Wang,
Gao, & Yuan. Following their inspirations, this dissertation introduces a subclass of
close-to-convex functions, denoted by Kk;N
s , where k;N 2 N, that combines the concepts
of S_ s and Ks and investigates them for their properties which include, but not limited to,
coefficient estimates, distortion and growth theorems, and radius of convexity. Moreover,
we also introduce the class of p-valent functions, denoted by Kk;N
s;p , in this dissertation which further generalizes the class Kk;N s and investigate it for its properties. In addition to investigating properties of geometric functions, many other mathematicians have also
expressed interest in finding sufficient conditions such that certain special functions has
certain geometric properties, such as univalency, starlikeness or convexity. Examples
of special functions that have undergone this investigation include Bessel and Struve
functions. Motivated by this, this dissertation also investigates sufficient conditions for
the function Tp;b;c(z) = (f _ gp;b;c)(z), a convolution between f(z) = z +
1P n=2 anzn and gp;b;c(z) = z + 1P
n=2
Properties of Functions Involving Struve Function
No full textLet f (z) = z + ∑n=2 ∞ anzn and gp,b,c(z) = z + ∑n=2 ∞ (-c4)n-1/(3/2)n-1(k)n-1zn with p, b, c ∈ C, k = p + b+2/2 ≠ 0,-1,-2, . . . be two analytic functions in the unit disk U = (z:|z| < 1). This paper gives conditions so that the function Tp,b,c(z) = ( f * g)(z), a function associated with the Struve function, is univalent, starlike, or convex in the unit disk
Properties of Functions Formed Using the Sakaguchi and Gao-Zhou Concept
No full textThis paper introduces a new class related to close-to-convex functions denoted by K s k , N . This class is based on combining the concepts of starlike functions with respect to N-ply symmetry points of the order α , introduced by Chand and Singh; and K s ( k ) , introduced by Wang, Gao, and Yuan, which are generalizations of the classes of functions introduced by Sakaguchi and Gao and Zhou, respectively. We investigate the class for several properties including coefficient estimates, distortion and growth theorems, and the radius of convexity
