Properties for Close-to-Convex and Quasi-Convex Functions Using q-Linear Operator - Ekram E. Ali; Rabha M. El-Ashwah; Abeer M. Albalahi; Wael W. Mohammed (Mathematics)
In this work, we describe the <semantics>q</semantics>-analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators <semantics><msubsup>Iq,ρs</msubsup>(ν,τ)</semantics>, and we obtain findings related to geometric function theory (GFT) by utilizing approaches established through subordination and knowledge of <semantics>q</semantics>-calculus operators. By using this operator, we develop generalized classes of quasi-convex and close-to-convex functions in this paper. Additionally, the classes <semantics><msubsup>Kq,ρs</msubsup>(ν,τ)<mfenced open="(" close=")">φ</mfenced></semantics>, <semantics><msubsup>Qq,ρs</msubsup>(ν,τ)<mfenced open="(" close=")">φ</mfenced></semantics> are introduced. The invariance of these recently formed classes under the <semantics>q</semantics>-Bernardi integral operator is investigated, along with a number of intriguing inclusion relationships between them. Additionally, several unique situations and the beneficial outcomes of these studies are taken into account.