Janowski Type <i>q</i>-Convex and <i>q</i>-Close-to-Convex Functions Associated with <i>q</i>-Conic Domain

• Main Authors: Muhammad Naeem, Saqib Hussain, Shahid Khan, Tahir Mahmood, Maslina Darus, Zahid Shareef
• Format: Article
• Language: English
• Published: MDPI AG 2020-03-01
• Series: Mathematics
• Subjects: analytic functions; janowski functions; conic domain; <i>q</i>-convex functions; <i>q</i>-close-to-convex functions
• Online Access: https://www.mdpi.com/2227-7390/8/3/440
• ISSN: 2227-7390

Certain new classes of <i>q</i>-convex and <i>q</i>-close to convex functions that involve the <i>q</i>-Janowski type functions have been defined by using the concepts of quantum (or <i>q</i>-) calculus as well as <i>q</i>-conic domain <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="(" close=")"> <msub> <mo>Ω</mo> <mrow> <mi>k</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> <mrow> <mo>[</mo> <mi>λ</mi> <mo>,</mo> <mi>α</mi> <mo>]</mo> </mrow> </mfenced> </semantics> </math> </inline-formula>. This study explores some important geometric properties such as coefficient estimates, sufficiency criteria and convolution properties of these classes. A distinction of new findings with those obtained in earlier investigations is also provided, where appropriate.