An Upper Bound for Third Hankel Determinant of Starlike Functions Related to Shell-like Curves Connected with Fibonacci Numbers
Journal Title: Journal of Mathematics and Applications - Year 2018, Vol 41, Issue
Abstract
We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions.
Authors and Affiliations
Janusz Sokół, Sedat İlhan, H. Özlem Güney
Keywords
Related Articles
- EP ID EP427013
- DOI 10.7862/rf.2018.14
- Views 84
- Downloads 0
Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells
Human T-cell Lymphotropic Virus I (HTLV-I) infection of CD4+ T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transf...
The Real and Complex Convexity
We prove that the holomorphic differential equation [formula] (φ: C → C be a holomorphic function and (γ,c) ∈ C^2) plays a classical role on many problems of real and complex convexity. The condition exactly [formula] (i...
On the Derivative of a Polynomial with Prescribed Zeros
For a polynomial [formula] of degree n having all its zeros in |z| ≤ K, K ≥ 1it is known that [formula]. By assuming a possible zero of order m, 0 ≤m ≤ n – 4, at z=0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have...
On circularly symmetric functions
Let D ⸦ C and 0 ∈ D. A set D is circularly symmetric if for each [formula] a set [formula] is one of three forms: an empty set, a whole circle, a curve symmetric with respect to the real axis containing ϱ. A function f...
Some New Existence Results and Stability Concepts for Fractional Partial Random Differential Equations
In the present paper we provide some existence results and Ulam's type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompac...