The main goal of this paper is to study applications of the fractional calculus techniques for a certain subclass of multivalent analytic functions on Hilbert Space. Also, we obtain the coefficient estimates, extreme points, convex combination and hadamard product.

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 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 further properties of the fuzzy complete a-fuzzy normed algebra have been introduced. Then we found the relation between the maximal ideals of fuzzy complete a-fuzzy normed algebra and the associated multiplicative linear function space. In this direction we proved that if  is character on Z then ker is a maximal ideal in Z. After this we introduce the notion structure of the a-fuzzy normed algebra then we prove that the structure, st(Z) is -fuzzy closed subset of fb(Z, ) when  (Z,  , , ) is a commutative fuzzy complete a-fuzzy normed algebra with identity e.

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 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 multiplicity of connotations in any paper does not mean that there is no main objective for that paper and certainly one of these papers is our research the main objective is to introduce a new connotation which is type-2 fuzzy somewhere dense set in general type-2 fuzzy topological space and its relationship with open sets of the connotation type-2 fuzzy set in the same space topology and theories of this connotation.

In this essay, we utilize m - space to specify m_X-N-connected, m_X-N-hyper connected and m_X-N-locally connected spaces and some functions by exploiting the intelligible m_X-N-open set. Some instances and outcomes have been granted to boost our tasks.

  In  this  paper, we  introduced   some  fact  in   2-Banach  space. Also, we define  asymptotically  non-expansive  mappings  in  the  setting  of  2-normed  spaces analogous  to  asymptotically non-expansive mappings  in  usual  normed spaces. And then prove the existence of fixed points for this type of mappings in 2-Banach spaces.