The study of fixed points on the  maps fulfilling certain contraction requirements has several applications and has been the focus of numerous research endeavors. On the other hand, as an extension of the idea of the best approximation, the best proximity point (ƁƤƤ) emerges. The best approximation theorem ensures the existence of an approximate solution; the best proximity point theorem is considered for addressing the problem in order to arrive at an optimum approximate solution. This paper introduces a new kind of proximal contraction mapping and establishes the best proximity point theorem for such mapping in fuzzy normed space ( space). In the beginning, the concept of the best proximity point was introduced. The concept of prox

         In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved  fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact

In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct  space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set  named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on  is also introduced with the prove that a fuzzy seminorm on

    In this paper, we prove some coincidence and common fixed point theorems for a pair of discontinuous weakly compatible self mappings satisfying generalized contractive condition in the setting of Cone-b- metric space under assumption that the Cone which is used is nonnormal. Our results are generalizations of some recent results.

       In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

   In this paper we prove a theorem about the existence and uniqueness common fixed point for two uncommenting self-mappings which defined on orbitally complete G-metric space. Where we use a general contraction condition.
 

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.

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators

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