In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.

In this work, we apply the notion of a filter of a KU-Algebra and investigate several properties. The paper defined some filters such as strong filter, n-fold filter and P-filter and discussed a few theorems and examples.

     In this article, an attempt has been made to introduce the concept of Neutrosophic d-Filter and Neutrosophic Prime d-Filter of d-Algebra by generalizing the notion of Intuitionistic Fuzzy d-Filter of d-Algebra. Besides, we establish different properties of them. Further, we study several relations on this notion from the point of view of Neutrosophic d-Algebra.

In the present paper, the concepts of a quasi-metric space, quasi-Banach space
have been introduced. We prove some facts which are defined on these spaces and
define some polynomials on quasi-Banach spaces and studied their dynamics, such
as, quasi cyclic and quasi hypercyclic. We show the existence of quasi chaotic in the
sense of Devaney (quasi D-chaotic) polynomials on quasi Banach space of qsummable
sequences lq , 0<q<1 such polynomials P is defined by P((xi)i)=(p(xi+m))i
where p:CC, p(0) = 0. In general we also prove that P is quasi chaotic in the sense
of Auslander and Yorke (quasi AY-chaotic) if and only if 0 belong to the Julia set of
p, mN. And then we prove that if the above polynomial P o

Sufficient conditions for boundary controllability of nonlinear system in quasi-Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and some techniques of nonlinear functional analysis, such as, fixed point theorem and quasi-Banach contraction principle theorem. Moreover, we given an example which is provided to illustrate the theory.

      In this paper, we introduced module that satisfying strongly -condition modules and strongly -type modules as generalizations of t-extending. A module  is said strongly -condition if for every submodule of  has a complement which is fully invariant direct summand. A module   is said to be strongly -type modules if every t-closed submodule has a complement which is a fully invariant direct summand. Many characterizations for modules with strongly -condition for strongly -type module are given. Also many connections between these types of module and some related types of modules are investigated.

Let R be a commutative ring with unity 1 6= 0, and let M be a unitary left module over R. In this paper we introduce the notion of epiform∗ modules. Various properties of this class of modules are given and some relationships between these modules and other related modules are introduced.

Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.

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 aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra  without identity can be embedded into fuzzy normed algebra  with identity  and  is an ideal in  is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.