Certain results for a class of convex functions related to a shell-like curve connected with Fibonacci numbers

摘要

This paper investigates some basic geometric properties for the class K&￡ of functions f analytic in the open unit disc Δ = {z : |z| < 1} (which is related to a shell-like curve and associated with Fibonacci numbers) satisfying the condition that f(0) = 0, f~'(0) = 1 and zf~('')(z)/f~'(z)<(ιz+ 2ι~2z~2)/(1-ιz-ι~2z~2) (z∈Δ), where, the number ι = (1 - √5)/2 is such that | ι | fulfils the golden section of the segment [0,1], Some relevant remarks and useful connections of the main results are also pointed out.