On α-convex functions related to shell-like functions connected with Fibonacci numbers

This paper presents a new class SLMαSLMα of functions f(z  ) analytic and normalized in the open unit disc U={z:|z|<1}U={z:|z|<1} (which is related to a shell-like curve and associated with Fibonacci numbers) satisfying the condition thatα1+zf″(z)f′(z)+(1-α)zf′(z)f(z)∈p˜(U)(z∈U),where α is a real number andp˜(z)=τz+τ2z21-τz-τ2z2(τ=(1-5)/2;z∈U).The class SLMαSLMα being closely related to the classes of starlike and convex functions, we apply some basic techniques to investigate certain interesting properties (given below) for this class of functions. Some important observations of the main results are also mentioned.