Abstract
In this paper, by making use the second kind Chebyshev polynomials, we introduce and study a certain class of bi-starlike and bi-convex functions with respect to symmetrical points defined in the open unit disk. We find upper bounds for the second and third coefficients of functions belong to this class.
Highlights
The importance of Chebyshev polynomial in numerical analysis is increased in both theoretical and practical points of view
Several researchers dealing with orthogonal polynomials of Chebyshev family, contain mainly results of Chebyshev polynomials of first kind Tn (t ), the second kind Un (t) and their numerous uses in different applications one can refer [5, 7, 9]
Sakaguchi [11] introduced the class Ss∗ of functions starlike with respect to symmetric points, which consists of functions f ∈ S satisfying the condition
Summary
The importance of Chebyshev polynomial in numerical analysis is increased in both theoretical and practical points of view. There are four kinds of Chebyshev polynomials. The Chebyshev polynomials of the first and second kinds are well known and they are defined by (− 1 < t < 1), where n indicates the polynomial degree and t = cos nθ.
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