The Second Hankel Determinant Problem for a Class of Bi-Close-to-Convex Functions

• Main Authors: Nak Eun Cho, Ebrahim Analouei Adegani, Serap Bulut, Ahmad Motamednezhad
• Format: Article
• Language: English
• Published: MDPI AG 2019-10-01
• Series: Mathematics
• Subjects: univalent function; second hankel determinant; subordination; close-to-convex functions; bi-close-to-convex functions
• Online Access: https://www.mdpi.com/2227-7390/7/10/986
• ISSN: 2227-7390

The purpose of the present work is to determine a bound for the functional <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>H</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msub> <mi>a</mi> <mn>4</mn> </msub> <mo>&#8722;</mo> <msubsup> <mi>a</mi> <mrow> <mn>3</mn> </mrow> <mn>2</mn> </msubsup> </mrow> </semantics> </math> </inline-formula> for functions belonging to the class <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">C</mi> <mo>&#931;</mo> </msub> </semantics> </math> </inline-formula> of bi-close-to-convex functions. The main result presented here provides much improved estimation compared with the previous result by means of different proof methods than those used by others.