Muhammet KAMALI, Mirzaolim TURABAEV, Erhan DENİZ, Murat ÇAĞLAR

Fekete-Szegö problem for a new subclass of analytic functions satisfying subordinate condition associated with Chebyshev polynomials

In this paper,we define a class of analytic functions F(β,λ) (H, α, δ, µ), satisfying the following subordinate condition associated with Chebyshev polynomials   α [ zG′ (z) G (z) ]δ + (1 − α) [ zG′ (z) G (z) ]µ [ 1 + zG′′ (z) G ′ (z) ]1−µ    ≺ H (z, t), where G (z) = λβz2 f ′′ (z) + (λ − β) zf′ (z) + (1 − λ + β) f (z), 0 ≤ α ≤ 1, 1 ≤ δ ≤ 2, 0 ≤ µ ≤ 1, 0 ≤ β ≤ λ ≤ 1 and t ∈ ( 1 2 , 1 ] . We obtain initial coefficients |a2| and |a3| for this subclass by means of Chebyshev polynomials expansions of analytic functions in D. Furthermore, we solve Fekete-Szegö problem for functions in this subclass.We also provide relevant connections of our results with those considered in earlier investigations. The results presented in this paper improve the earlier investigations.

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