Browsing by Author "Bulut, Serap"

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    Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions
    (Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Bulut, Serap; Other; Other
    Considering a new subclass of m-fold symmetric analytic bi-univalent functions, we determine estimates the coefficient bounds for the Taylor-Maclaurin coefficients |a_{m+1}| and |a_{2m+1}| of the functions in this class. In certain cases, our estimates improve some of those existing coeffcient bounds.
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    Logarithmic coefficients of starlike functions connected with k-Fibonacci numbers
    (Ankara Üniversitesi, 2021) Bulut, Serap; Other; Other
    Let A denote the class of analytic functions in the open unit disc U normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 , and let S be the class of all functions f ∈ A which are univalent in U . For a function f ∈ S , the logarithmic coefficients δ n ( n = 1 , 2 , 3 , … ) are defined by log f ( z ) z = 2 ∑ ∞ n = 1 δ n z n ( z ∈ U ) . and it is known that | δ 1 | ≤ 1 and | δ 2 | ≤ 1 2 ( 1 + 2 e − 2 ) = 0 , 635 ⋯ . The problem of the best upper bounds for | δ n | of univalent functions for n ≥ 3 is still open. Let S L k denote the class of functions f ∈ A such that z f ′ ( z ) f ( z ) ≺ 1 + τ 2 k z 2 1 − k τ k z − τ 2 k z 2 , τ k = k − √ k 2 + 4 2 ( z ∈ U ) . In the present paper, we determine the sharp upper bound for | δ 1 | , | δ 2 | and | δ 3 | for functions f belong to the class S L k which is a subclass of S . Furthermore, a general formula is given for | δ n | ( n ∈ N ) as a conjecture.
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    Quasi-subordination and coefficient bounds for certain classes of meromorphic functions of complex order
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Zayed, H. M.; Bulut, Serap; Mostafa, A. O.; Other; Other
    In this paper, we obtain Fekete-Szegö functional |a₁-μa₀²| for functions of the classes Σ_{q}^{∗}(ϕ) and Σ_{q,λ,b}^{∗}(g,ϕ) using quasi-subordination. Sharp bounds for the Fekete-Szegö functional |a₁-μa₀²| are obtained. Also, applications of the main results for subclasses of functions defined by Bessel function are also considered.