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COEFFICIENT INEQUALITIES FOR ANALYTIC FUNCTIONS CONNECTED WITH k-FIBONACCI NUMBERS

  • Serap, Bulut (Kocaeli University, Faculty of Aviation and Space Sciences) ;
  • Janusz, Sokol (University of Rzeszow, College of Natural Sciences)
  • Received : 2022.04.01
  • Accepted : 2022.10.04
  • Published : 2022.12.25
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Abstract

In this paper, we introduce a new class 𝓡kλ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ∞n=2 anzn (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡kλ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a3-𝜇a22| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

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References

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