Janowski-type mappings associated with the conic like 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 U_kS(λ, γ, τ, ρ) and U ^ℑ _k 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 ∈ U_kS(λ, γ, τ, ρ) along with the characterization, coefficient bounds and other problems. Using certain conditions for functions in the class U_kS(λ, γ, ϱ, σ), we also define another class and study some subordination related result. [ABSTRACT FROM AUTHOR]