Regular classes involving a generalized shift plus fractional Hornich integral operator

Abstract

The Hornich space is the set of all locally univalent and analytic functions Á on the open unit disk such that argÁ0 is bounded. Here, we introduce a generalized integral operator in the open unit disk. This operator is dened by the fractional Hornich integral operator joining the shift plus multiplier. In addition, we deal with a new subspace of the Hardy space comprising the normalized analytic functions. We will validate that the new integral operator is closed in the subspace of normalized functions with the bounded rst derivative. Formal accounts are renowned in the sequel based on the maximally of Jack Lemma.