The purpose of the present paper is to introduce two new subclasses of the function class ∑m  of bi-univalent functions which both f  and f-1  are m-fold symmetric analytic functions. Furthermore, we obtain estimates on the initial coefficients for functions in each of these new subclasses. Also we explain the relation between our results with earlier known results.

In this paper, using the Steklov function, we introduce the generalized continuity modulus and denethe class of functions Wr;kp;' in the space Lp. For this class, we prove an analog of the estimates in [1]in the space Lp.

a characteriation of continuity of the $p$-$lambda$-variation function is given and the helly's selection principle for $lambda bv^{(p)}$ functions is established. a characterization of the inclusion of waterman-shiba classes into classes of functions with given integral modulus of continuity is given. a useful estimate on modulus of variation of functions of class $lambda bv^{(p)}$ is found.

Abstract We consider a real-valued function f defined on the set of infinite branches X countably branching pruned tree T . The is said to be limsup if there $u \colon \to \mathbb {R}$ such that $f(x) = \limsup _{t \infty } u(x_{0},\dots ,x_{t})$ for each $x \in X$ study game characterization functions, as well novel functions Baire class 1.

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

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.