LAUSR

Using the idea of convolution between analytic functions, we define a class $$\mathcal {UM}(g,\gamma ,b,k)$$UM(g,γ,b,k) of analytic functions comprising of starlike and convex functions. These functions map the open unit disc on to the conic domains. We derive some sufficient conditions and then use them to define the class $$\mathcal {UM}^{*}(g,\gamma ,b,k)$$UM∗(g,γ,b,k). Making use of an increasing factor sequence, we discuss a subordination result. We may relate our findings with the previously known results.