In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

In this work we define and study new concept of fibrewise topological spaces, namely fibrewise soft topological spaces, Also, we introduce the concepts of fibrewise closed soft topological spaces, fibrewise open soft topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces.

R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>

Internal control system is a safety valve that preserves economic units assets and ensure the accuracy of financial data, as well as to obligation in the laws, regulations, administrative policies ,and improve the efficiency, effectiveness and economic of operation, so it has become imperative for these units attention to internal and developed control system The research problem in exposure the economic units when the exercise of their business to many of the risks to growth or hinder the achievement of its objectives and the risks (financial, operational, strategy, risk) and not it rely on risk Assessment according to modern scientific methods, as in Brown's risk Classification, Which led to the weakness of the internal control identif

The purpose of this paper is to study a new types of compactness in the dual bitopological spaces. We shall introduce the concepts of L-pre- compactness and L-semi-P- compactness .