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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.