In this paper, subclasses of  the function class  ∑  of analytic and bi-univalent functions associated with operator  L_q^(k,  λ)  are introduced and defined in the open unit disk △ by applying quasi-subordination. We obtain some results about the corresponding bound estimations of the coefficients  a_(2 )  and a_(3 ).

In this paper introduce some generalizations of some definitions which are, closure converge to a point, closure directed toward a set, almost ω-converges to a set, almost condensation point, a set ωH-closed relative, ω-continuous functions, weakly ω-continuous functions, ω-compact functions, ω-rigid a set, almost ω-closed functions and ω-perfect functions with several results concerning them.

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .

    In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of

Let  be a commutative ring with 1 and  be a left unitary . In this paper, the generalizations for the notions of compressible module and  retractable module are given.

An   is termed to be  semi-essentially compressible if   can be embedded in every of a non-zero semi-essential submodules. An  is termed a semi-essentially retractable module, if   for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given.  We also study the relation between these classes and some other classes of modules.

We presented in this paper a new class containing analytic univalent functions defined on unit disk. We obtained many geometric properties , like , coefficient inequality , distortion and growth theorems, convolution property, convex set, arithmetic mean and radius of starlikness and convexity by using Gaussian hypergeometric function for the class

     In this paper we introduce a new class of sets called -generalized b- closed (briefly gb closed) sets. We study some of its basic properties. This class of sets is strictly placed between the class of gp- closed sets and the class of gsp- closed sets. Further the notion of b- space is introduced and studied.

2000 Mathematics Subject Classification: 54A05

In this paper by using δ-semi.open sets we introduced the concept of weakly δ-semi.normal and δ-semi.normal spaces . Many properties and results were investigated and studied. Also we present the notion of δ- semi.compact spaces and we were able to compare with it δ-semi.regular spaces

    In this paper, we derive some subordination and superordination results for certain subclasses of p− valent analytic functions that defined by generalized Fox-wright functions using the principle of differential subordination, ----------producing best dominant univalent solutions. We have also derived inclusion relations and solved majorization problem.