The concept of closed quasi principally injective acts over monoids is introduced ,which signifies a generalization for the quasi principally injective as well as for the closed quasi injective acts. Characterization of this concept is intended to show the behavior of a closed quasi principally injective property. At the same time, some properties of closed quasi principally injective acts are examined in terms of their endomorphism monoid. Also, the characterization of a closed self-principally injective monoid is given in terms of its annihilator. The relationship between the following concepts is also studied; closed quasi principally injective acts over monoids, Hopfian, co Hopfian, and directly finite property. Ultimately, based on

      In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left -module  over a commutative ring  with identity. This concept is a generalization of prime and primary submodules, where a proper submodule  of an -module  is called an approximaitly quasi-primary (for short App-qp) submodule of , if , for , , implies that either  or , for some . Many basic properties, examples and characterizations of this concept are introduced.

The purpose of this research is to introduce a concept of general partial metric spaces as a generalization of partial metric space. Give some results and properties and find relations between general partial metric space, partial metric spaces and D-metric spaces.

In this article, a new class  of analytic functions which is defined by terms of a quasi-subordination is introduced. The coefficient estimates, including the classical  inequality of functions belonging to this class, are then derived. Also, several special improving results for the associated classes involving the subordination are presented.

The aim of this research is to use the class of soft simply open set to define new types of separation axioms in soft topological spaces. We also introduce and study the concept of soft simply compactness.

In this paper, we will give another class of normal operator which is (K-N)*
quasi-n-normal operator in Hilbert space, and give some properties of this concept
as well as discussion the relation between this class with another class of normal
operators.

Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.

The concept of a 2-Absorbing submodule is considered as an essential feature in the field of module theory and has many generalizations. This articale discusses the concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules and their relationship to the 2-Absorbing submodule, Quasi-2-Absorbing submodule, Nearly-2-Absorbing submodule, Pseudo-2-Absorbing submodule, and the rest of the other concepts previously studied. The relationship between them has been studied, explaining that the opposite is not true and that under certain conditions the opposite becomes true. This article aims to study this concept and gives the most important propositions, characterizations, remarks, examples, lemmas, and observations related to it. In the en

     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.

      Throughout this paper, a generic iteration algorithm for a finite family of total asymptotically quasi-nonexpansive maps in uniformly convex Banach space is suggested. As well as weak / strong convergence theorems of this algorithm to a common fixed point are established. Finally, illustrative numerical example by using Matlab is presented.