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On certain generalized \(q\)-integral operators of analytic functions. (English) Zbl 1330.30025

Summary: In this article, we first consider a linear multiplier fractional \(q\)-differintegral operator and then use itto define new subclasses of \(p\)-valent analytic functions in the open unit disk \(\mathcal{U}\). An attempt has also been made to obtain two new \(q\)-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
26A33 Fractional derivatives and integrals
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