In this article, results have been shown via using a general quasi contraction multi-valued mapping in Cat(0) space. These results are used to prove the convergence of two iteration algorithms to a fixed point and the equivalence of convergence. We also demonstrate an appropriate conditions to ensure that one is faster than others.

The product  of   rn-paracompact and   rn-strongly  paracompact are briefly disc. ussed.

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.

The theory of general topology view for continuous mappings is general version and is applied for topological graph theory. Separation axioms can be regard as tools for distinguishing objects in information systems. Rough theory is one of map the topology to uncertainty. The aim of this work is to presented graph, continuity, separation properties and rough set to put a new approaches for uncertainty. For the introduce of various levels of approximations, we introduce several levels of continuity and separation axioms on graphs in Gm-closure approximation spaces.

      In this paper, we extend the work of our proplem in uniformly convex Banach spaces using Kirk fixed point theorem. Thus the existence and sufficient conditions for the controllability to general formulation of nonlinear boundary control problems in reflexive Banach spaces are introduced. The results are obtained by using fixed point theorem that deals with nonexpanisive mapping defined on a set has normal structure and strongly continuous semigroup theory. An application is given to illustrate the  importance of the results.

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 .

  The research addressed the formal functions resulting from the use of various guiding signs in the design of the interior spaces of airports in various pragmatic, expressive and psychological aspects. The aim is to identify the functions the guiding signs perform in facilitating and organizing the travelers' movement and satisfying the needs of the visitors and users of the unfamiliar places which they intend to visit, the nature of the services offered by these signs as one of the important parts within their general design. The research also identified the concept and types of signs as a means of visual communication and how to employ them in the design of the airports public spaces, and what are the criteria of their use and fu

In this article an attempt has been made to procure the concept of pairwise neutrosophic simply open set, pairwise neutrosophic simply continuous mapping, pairwise neutrosophic simply open mapping, pairwise neutrosophic simply compactness, pairwise neutrosophic simply b-open set, pairwise neutrosophic simply b-continuous mapping, pairwise neutrosophic simply b-open mapping and pairwise neutrosophic simply b-compactness via neutrosophic bi-topological spaces (in short NBTS). Besides, we furnish few illustrative examples on them via NBTS. Further, we investigate some basic properties of them, and formulate several results on NBTSs.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near compact and fibrewise locally near compact spaces, which are generalizations of well-known concepts near compact and locally near compact topological spaces. Moreover, we study relationships between fibrewise near compact (resp., fibrewise locally near compact) spaces and some fibrewise near separation axioms.