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 KSLKSL of functions ff analytic in the open unit disc Δ={z:|z|<1}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)=1andzf″(z)f′(z)≺τz+2τ2z21−τz−τ2z2(z∈Δ), where, the number τ=(1−5)/2 is such that |τ||τ| fulfils the golden section of the segment [0,1][0,1]. Some relevant remarks and useful connections of the main results are also pointed out.