UNIVALENCE STUDIES CONCERNING A NEW INTEGRAL OPERATOR INVOLVING BESSEL FUNCTION OF THE FIRST KIND

The present investigation enhances a basic theme in geometric function theory, namely introducing new operators and establishing geometric characterization properties of starlikeness and convexity for these operators. This paper presents a new integral operator defined by applying the fractional integral of the Bessel function of the first kind and order ν ≥ 0. The investigation establishes sufficient and necessary conditions for starlikeness and convexity of the newly introduced operator by applying specific techniques of the differential subordination theory and certain properties previously obtained for the fractional integral of the Bessel function of the first kind and order ν ≥ 0. Although a simple application example is provided, the starlikeness and convexity properties given here could motivate additional investigation on this operator for further applications in other lines of research in geometric function theory.