Bulut, Serap2022-12-232022-12-232021https://doi.org/10.31801/cfsuasmas.808319http://hdl.handle.net/20.500.12575/86418Let 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.enAnalytic function, univalent function, shell-like function, logarithmic coefficients, k-Fibonacci number, subordinationArticle7029109231303-5991