In this paper, we define a new subclass of multivalent functions defined by the generalized integral operator with negative coefficients in the open unit disk U. We also give and study some interesting properties such as coefficient estimates, subordination theorems and integral means inequalities by using the famous Littlewood's subordination theorem. Finally, we conclude a type of inequalities that is upper bound and lower bound for topology multivalent functions of all analytic functions.  

     This paper aims to introduce the concepts of  -closed, -coclosed, and -extending modules as generalizations of the closed, coclossed, and extending modules,  respectively. We will prove some properties as when the image of the e*-closed submodule is also e*-closed and when the submodule of the e*-extending module is e*-extending. Under isomorphism, the e*-extending modules are closed. We will study the quotient of e*-closed and e*-extending, the direct sum of e*-closed, and the direct sum of e*-extending.

     Let Ḿ be a unitary R-module and R is a commutative ring with identity. Our aim in this paper  to study the concepts T-ABSO fuzzy ideals, T-ABSO fuzzy submodules and T-ABSO quasi primary fuzzy submodules, also we discuss these concepts in the class of multiplication fuzzy modules and relationships between these concepts. Many new basic properties and characterizations on these concepts are given.

   Let R be a ring with identity and Ą a left R-module. In this article, we introduce new generalizations of compressible and prime modules, namely s-compressible module and s-prime module. An R-module A is s-compressible if for any nonzero submodule B of A there exists a small f in Hom_R(A, B). An R-module A is s-prime if for any submodule B of A, ann_R (B) A is small in A. These concepts and related concepts are studied in as well as  many results consist properties and characterizations are obtained.  

Often phenomena suffer from disturbances in their data as well as the difficulty of formulation, especially with a lack of clarity in the response, or the large number of essential differences plaguing the experimental units that have been taking this data from them. Thus emerged the need to include an estimation method implicit rating of these experimental units using the method of discrimination or create blocks for each item of these experimental units in the hope of controlling their responses and make it more homogeneous. Because of the development in the field of computers and taking the principle of the integration of sciences it has been found that modern algorithms used in the field of Computer Science genetic algorithm or ant colo

In thisipaper, we introduce the concepts of the modified tupledicoincidence points and the  mixed finiteimonotone property. Also the existenceiand uniquenessiof modified tupled coincidenceipoint is discusses without continuous condition for mappings having imixed finite monotoneiproperty in generalizedimetric spaces.

     In this paper, we define and study z-small quasi-Dedekind as a generalization of small quasi-Dedekind modules. A submodule  of -module  is called z-small (  if whenever  , then . Also,  is called a z-small quasi-Dedekind module if for all  implies  . We also describe some of their properties and characterizations. Finally, some examples are given.

An -module is called absolutely self neat if whenever is a map from a maximal left ideal of , with kernel in the filter is generated by the set of annihilator left ideals of elements in into , then is extendable to a map from into . The concept is analogous to the absolute self purity, while it properly generalizes quasi injectivity and absolute neatness and retains some of their properties. Certain types of rings are characterized using this concept. For example, a ring is left max-hereditary if and only if the homomorphic image of any absolutely neat -module is absolutely self neat, and is semisimple if and only if all -modules are absolutely self neat.

      In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout this work, we assume that    is a commutative ring with identity and  is a left unitary R- module. A  proper submodule  of  is called a quasi-radical semi prime submodule (for short Q-rad-semiprime), if     for   ,   ,and then  . Where   is the intersection of all prime submodules of .

In this note we consider a generalization of the notion of a purely extending
modules, defined using y– closed submodules.
We show that a ring R is purely y – extending if and only if every cyclic nonsingular
R – module is flat. In particular every nonsingular purely y extending ring is
principal flat.