Initial coefficients and fourth Hankel determinant for certain analytic functions

[摘要] The present work is an attempt to give partial proofs of certain conjectures on the fifth coefficient of certain normalized analytic functions. Further, bounds on the sixth and seventh coefficients for the starlike functions related to a lune are also investigated. The non-sharp bound on third and fourth Hankel determinants are also obtained.

[学科分类] 数学（综合）

[关键词] starlike functions;third Hankel determinant;fourth Hankel determinant;initial coefficients