Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator

Ibrahim, Rabha W.

Research Article

Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator

Rabha W. Ibrahim¹

Abstract

In this effort, we deal with a new integral operator in the open unit disk. This operator is formulated by the complex Alexander operator and its derivative. Furthermore, we introduce a new subspace of the Hardy space containing the normalized analytic functions. We shall prove that the new integral operator is closed in the subspace of normalized functions. Geometric characterizations are established in the sequel based on the maximality of Jack Lemma.

How to Cite

R. W. Ibrahim, Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator, Int. J. Anal. Appl. 14 (2017), 34–41.

BibTeX

@article{Ibrahim2017,
  author  = {Ibrahim, Rabha W.},
  title   = {Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator},
  journal = {Int. J. Anal. Appl.},
  volume  = {14},
  year    = {2017},
  pages   = {34--41},
  doi     = {}
}

References

[1] J.W. Alexsander, Functions which map the interior of the unit circle upon simple regions, Ann. Math., 17(1915), 12-22.
[2] S.S. Miller and P.T. Mocanu, Differential Subordinations: Theory and Applications, Mrcel Dekker Inc., New York, 2000.
[3] C. Zeljko and B. Paudyal, Invariant subspaces of the shift plus complex Volterra operator, J. Math. Anal. Appl. 426(2)(2015), 1174-1181.
[4] I.S. Jack, Functions starlike and convex of order α, J.London Math. Soc. 3(1971), 469-474.
[5] P.L. Duren., Univalent Functions, Springer-Verlag, 1983.