| Summary: | As an application of the well-known Sălăgean differential operator, a new operator is introduced and, using this, a new class of functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>n</mi></msub><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is defined, which has the classes of starlike and convex functions of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> as special cases. Original results related to the newly defined class are obtained using the renowned Jack–Miller–Mocanu lemma. A relevant example is given regarding the applications of a new proven result concerning interesting properties of class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>n</mi></msub><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>.
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