Properties of close-to-convex functions and special functions / Jonathan Aaron Azlan Mosiun
Let 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 exten...
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| Format: | Thesis |
| Published: |
2019
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| Subjects: | |
| Online Access: | http://studentsrepo.um.edu.my/11845/2/Jonathan.pdf http://studentsrepo.um.edu.my/11845/1/Jonathan_Aaron.pdf http://studentsrepo.um.edu.my/11845/ |
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| Summary: | Let 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
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