janowski-type mappings associated with the conic shaped domains

In geometry, a conic is a plane curve whose coordinates satisfy a quadratic equation in two variables and can be expressed in matrix form. this equation allows deducing and expressing geometric properties of conic sections. in this article, we define certain subclasses uks(λ, γ, τ, ρ) and uℑk s(λ, γ, τ, ρ) of holomorphic mappings associated with the janowski-type mappings. these functions are actually generalizations of some basic families of starlike and convex mappings. we study sufficient conditions for f ∈ uks(λ, γ, τ, ρ) along with the characterization, coefficient bounds and other problems. using certain conditions for functions in the class uks(λ, γ, ϱ, σ), we also define another class and study some subordination related result.