The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

     The concept of separation axioms constitutes a key role in general topology and all generalized forms of topologies. The present authors continued the study of gpα-closed sets by utilizing this concept, new separation axioms, namely gpα-regular and gpα-normal spaces are studied and established their characterizations. Also, new spaces namely gpα-T_k  for k = 0, 1, 2 are studied.

In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.

    In this paper, new concepts of maximal and minimal regular s are introduced and discussed. Some basic properties are obtained. The relation between maximal and minimal regular s and some other types of open sets such as regular open sets and   -open sets are investigated.

     This paper introduces cutpoints and separations in -connected topological spaces, which are constructed by using the union of vertices set and edges set for a connected graph, and studies the relationships between them. Furthermore, it generalizes some new concepts.

     In this paper we introduce a new class of sets called -generalized b- closed (briefly gb closed) sets. We study some of its basic properties. This class of sets is strictly placed between the class of gp- closed sets and the class of gsp- closed sets. Further the notion of b- space is introduced and studied.

2000 Mathematics Subject Classification: 54A05

The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result. 

 In this paper, we introduce and study the concept of a new class of generalized closed set which is called generalized b*-closed set in topological spaces ( briefly .g b*-closed) we study also. some of its  basic properties and investigate the relations between the associated topology. 

     The problem in the design of a cam is the analyzing of the mechanisms and dynamic forces that effect on the family of parametric polynomials for describing the motion curve. In present method, two ways have been taken for optimization of the cam size, first the high dynamic loading (such that impact and elastic stress waves propagation) from marine machine tool which translate by the roller follower to the cam surface and varies with time causes large contact loads and second it must include the factors of kinematics features including the acceleration, velocity, boundary condition and the unsymmetrical curvature of the cam profile for the motion curve.

     In the theoretical solution