Univalence of Criteria for Linear Fractional Differential Operator $D_{\lambda}^{n,\alpha}$ With the Bessel Function

TL;DR

This paper extends and refines conditions under which certain integral operators involving generalized Bessel functions are univalent within the unit disk, enhancing previous theoretical results.

Contribution

It introduces improved sufficient conditions for the univalence of integral operators with generalized Bessel functions, broadening the scope of prior findings.

Findings

Established new sufficient conditions for univalence.

Extended previous results to more general operators.

Provided theoretical proofs supporting the conditions.

Abstract

In this paper our aim is to extend and improve the sufficient conditions for integral operators involving the normalized forms of the generalized Bessel functions of the first kind to be univalent in the open unit disk as investigated recently by (Erhan, E. Orhan, H. and Srivastava, H. (2011). Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions. Taiwanese Journal of Mathematics, 15 (2), pp.883-917) and (Baricz, \'A. and Frasin, B. (2010). Univalence of integral operators involving Bessel functions. Applied Mathematics Letters, 23 (4), pp.371-376).