| Summary: | In our present investigation, with the help of the basic (or <i>q</i>-) calculus, we first define a new domain which involves the Janowski function. We also define a new subclass of the class of <i>q</i>-starlike functions, which maps the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">U</mi></semantics></math></inline-formula>, given by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">U</mi><mo>=</mo><mo> </mo><mfenced separators="" open="{" close="}"><mi>z</mi><mo>:</mo><mi>z</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi><mo> </mo><mi>and</mi><mo> </mo><mfenced open="|" close="|"><mi>z</mi></mfenced><mo> </mo><mo><</mo><mn>1</mn></mfenced><mo>,</mo></mrow></semantics></math></inline-formula> onto this generalized conic type domain. We study here some such potentially useful results as, for example, the sufficient conditions, closure results, the Fekete-Szegö type inequalities and distortion theorems. We also obtain the lower bounds for the ratio of some functions which belong to this newly-defined function class and for the sequences of the partial sums. Our results are shown to be connected with several earlier works related to the field of our present investigation. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter <i>p</i> is obviously redundant.
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