Logarithmic coefficients of starlike functions connected with k-Fibonacci numbers

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dc.contributor.authorBulut, Serap
dc.contributor.departmentOthertr_TR
dc.contributor.facultyOthertr_TR
dc.date.accessioned2022-12-23T12:00:55Z
dc.date.available2022-12-23T12:00:55Z
dc.date.issued2021
dc.description.abstractLet 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.tr_TR
dc.description.indexTrdizintr_TR
dc.identifier.endpage923tr_TR
dc.identifier.issn/e-issn1303-5991
dc.identifier.issue2tr_TR
dc.identifier.startpage910tr_TR
dc.identifier.urihttps://doi.org/10.31801/cfsuasmas.808319tr_TR
dc.identifier.urihttp://hdl.handle.net/20.500.12575/86418
dc.identifier.volume70tr_TR
dc.language.isoentr_TR
dc.publisherAnkara Üniversitesitr_TR
dc.relation.isversionof10.31801/cfsuasmas.808319tr_TR
dc.relation.journalCommunications, Series A1:Mathematics and Statisticstr_TR
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıtr_TR
dc.subjectAnalytic function, univalent function, shell-like function, logarithmic coefficients, k-Fibonacci number, subordinationtr_TR
dc.titleLogarithmic coefficients of starlike functions connected with k-Fibonacci numberstr_TR
dc.typeArticletr_TR

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Cilt:70 Sayı:02 (2021)