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The aim of this article is to estimate an upper bound of |𝐻_3(1)|, the Zalcman coefficient functional for 𝑛 = 3 and 𝑛 = 4, and also to investigate the fifth, sixth, seventh coefficients of starlike and convex functions associated with shell-like curves. Similar type of outcomes are estimated for the functions 𝑓^(−1) and 𝑧/𝑓(𝑧).