Summary: | In the current paper, we study a majorization issue for a general category <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi mathvariant="script">S</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>ϑ</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> of starlike functions, the region of which is often symmetric with respect to the real axis. For various special symmetric functions <inline-formula> <math display="inline"> <semantics> <mi>ϑ</mi> </semantics> </math> </inline-formula>, corresponding consequences of the main result are also presented with some relevant connections of the outcomes rendered here with those obtained in recent research. Moreover, coefficient bounds for some majorized functions are estimated.
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