Janowski-type mappings associated with the conic shaped domain

Document Type : Research Paper


Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur-10250(AJK), Pakistan


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 $\mathcal{U}_{k}\mathcal{S} (\lambda,\gamma,\tau,\rho)$ and  $\mathcal{U}_{k}^{\Im}\mathcal{S}(\lambda,\gamma,\tau,\rho)$ 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 $f\in \mathcal{U}_{k}\mathcal{S}(\lambda,\gamma,\tau,\rho)$ along with the characterization, coefficient bounds and other problems. Using certain conditions for functions in the class $\mathcal{U}_{k}\mathcal{S}(\lambda,\gamma,\varrho,\mathbb{\sigma}),$ we also define another class and study some subordination related result.


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Volume 13, Issue 2
July 2022
Pages 2469-2478
  • Receive Date: 10 November 2021
  • Accept Date: 13 June 2022