In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.

in this work, we obtain the fekete-szegö inequalities for the class $p_{sigma }left( lambda ,phi right) $ of bi-univalent functions. the results presented in this paper improve the recent work of prema and keerthi [11].

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

In this work, we obtain the Fekete-Szegö inequalities for the class $P_{Sigma }left( lambda ,phi right) $ of bi-univalent functions. The results presented in this paper improve the recent work of Prema and Keerthi [11].

The well-known Schwarz–Pick lemma states that any analytic mapping φ of the unit disk U into itself satisfies the inequality |φ′(z)| ≤ 1− |φ(z)| 2 1− |z|2 , z ∈ U. This estimate remains the same if we restrict ourselves to univalent mappings. The lower estimate is |φ′(z)| ≥ 0 generally or |φ′(z)| > 0 for univalent functions. To make the lower estimate nontrivial we consider univalent functions ...

in this paper‎, ‎we introduce a new class$t_{k}^{s,a}[a,b,alpha‎ ,‎beta ]$ of analytic functions by using a‎ ‎newly defined convolution operator‎. ‎this class contains many known classes of‎ ‎analytic and univalent functions as special cases‎. ‎we derived some‎ ‎interesting results including inclusion relationships‎, ‎a radius problem and‎ ‎sharp coefficient bound for this class‎.