Coefficient estimates and Fekete-Szegö inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials

Abstract

Abstract In this paper, we define a class of analytic functions, ℱ(ℋ, α, δ, µ), satisfying the following condition (α[ zf′(z)f(z) ]δ+(1-α)[ zf′(z)f(z) ]μ[ 1+zf″(z)f′(z) ]1-μ)≺𝒣(z,t), \left( {\alpha {{\left[ {{{{\rm{zf'}}({\rm{z}})} \over {{\rm{f}}(z)}}} \right]}^\delta } + (1 - \alpha ){{\left[ {{{{\rm{zf'}}\left( {\rm{z}} \right)} \over {{\rm{f}}(z)}}} \right]}^\mu }{{\left[ {1 + {{{\rm{zf''}}({\rm{z}})} \over {{\rm{f'}}({\rm{z}})}}} \right]}^{1 - \mu }}} \right)\,\, \prec \mathcal{H}({\rm{z}},{\rm{t}}), where α ∈ [0, 1], δ ∈ [1, 2] and µ ∈ [0, 1]. We give coefficient estimates and Fekete-Szegö inequality for this class.