On the preservation of the boundedness of the $l$-index under the action of the Bernardi integral operator and the Ruscheweyh derivative
DOI:
https://doi.org/10.31471/2304-7399-2026-22(83)-29-35Keywords:
univalent function; bounded $l$-index; Bernardi integral operator; Ruscheweyh derivativeAbstract
We study the action of the Bernardi integral operator and the Ruscheweyh derivative on analytic functions of bounded $l$-index in a disc. Sufficient conditions are given for functions of bounded $l$-index under which their images under the action of the Bernardi integral operator, as well as the Rusheweyh derivative operator, are also functions of bounded $l$-index with the same function $l$. The proof is based on the theorem of M.M. Sheremeta and Z.M. Sheremeta (1999), which contains a sufficient condition for the boundedness of the l-index of an analytic function in a disc. It is formulated in the form of a restriction on the Taylor coefficients of a given analytic function of bounded $l$-index.References
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