Abstract
We introduce a class \({\mathfrak {R}}_{\alpha }^{q}\) of q-prestarlike functions of order \(\alpha \) by using q-difference operator. We obtain necessary and sufficient conditions involving convolution for functions to be in the class \({\mathfrak {R}}_{\alpha }^{q}.\) We prove that the well-known class of analytic prestarlike functions, \({\mathfrak {R}}_{\alpha },\) is properly contained in \({\mathfrak {R}}_{\alpha }^{q}.\) Apart from finding bounds on some initial coefficients of functions in the class \({\mathfrak {R}}_{\alpha }^{q}\), we also investigate some convolution properties of functions in the class \({\mathfrak {R}}_{\alpha }^{q}.\) The results of the present manuscript essentially generalize some well-known results in the literature.
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S.V. and R.K. developed the idea of analog class of prestarlike functions using q-derivatives and discussed it with O.P. and A.C. Further, all the authors contributed significantly to obtain main results of the present manuscript and have reviewed the manuscript carefully.
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Verma, S., Kumar, R., Ahuja, O.P. et al. q-Analog of prestarlike functions. Complex Anal Synerg 10, 11 (2024). https://doi.org/10.1007/s40627-024-00137-x
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DOI: https://doi.org/10.1007/s40627-024-00137-x