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

This paper investigates some basic geometric properties for the class KSL of functions f analytic in the open unit disc @D={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)=1andzf^''(z)f^'(z)@[email protected][email protected]^2z^[email protected]@t^2z^2([email protected][email protected]), where, the number @t=(1-5)/2 is such that |@t| fulfils the golden section of the segment [0,1]. Some relevant remarks and useful connections of the main results are also pointed out.