Some fixed point theorems in fuzzy normed linear spaces

In this paper, the concepts of sectional fuzzy continuous mappings, l-fuzzy compact sets, asymptotic fuzzy normal structure and strong uniformly convex fuzzy normed linear spaces have been introduced. Schauder-type and other fixed point theorems have been established in fuzzy normed linear spaces.     

Stability of mixed type functional equation in normed spaces using fuzzy concept

S. M. Ulam once addressed the problem ‘when is it true that a mathematical object satisfying a certain property approximately must be close to an object satisfying the property exactly?’. This problem was solved by D. H. Hyers in 1941 using the functional equation and thereafter numerous research papers and monographs have been published for various types of functional equations in different spaces. The solution proposed by D. H. Hyers (1941) later developed into the famous generalized Hyers-Ulam-Rassias stability of functional equations. In this paper, we intend to attain the general solution to a new mixed type functional equation and interrogate the generalized Hyers–Ulam–Rassias stability in fuzzy normed spaces. Also, we seek to provide its application for generating secret keys in client–server environment.     

Fixed point theorem of generalized quasi-contractive mapping in cone metric space

In this paper, we introduce the generalized quasi-contractive mapping f in a cone metric space (X,d). f is called a generalized quasi-contractive if there is a real λ∈[0,1) such that for all x,y∈X,

d(fx,fy)≤λs     

Strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in Banach spaces

In this paper, we introduce a new iterative algorithm by a modified extragradient method for finding a common element of the set of solutions of a general variational inequality and the set of common fixed points of an infinite family of k_i-strict pseudocontractions in a Banach space. We obtain some strong convergence theorems under suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others.     

An iterative approximation scheme for solving a split generalized equilibrium,variational inequalities and fixed point problems

In this paper, we consider a common solution of three problems in Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and fixed point problem. For finding the solution, we present a new iterative method and prove the strongly convergence theorem under mild conditions. Moreover, some numerical examples are given in the last section.     

A discussion on “Calculating fuzzy inverse matrix using fuzzy linear equation system”

In the present note it is shown that the examples presented in a recent paper by Basaran are incorrect. The correct exact solutions are also presented here. In this way, a new direction for approximating fuzzy inverse matrix is proposed. In this paper, the first step we solve the center part of fully fuzzy linear system, then we solve the spread part of the equation system.     

基于模糊线性回归的脑卒中发病率预测模型

针对经典线性回归模型不能完全反映变量间的耦合关系而不适宜有模糊数的脑卒中发病率预测的问题,建立了一种模糊多元线性回归分析的脑卒中发病率预测模型。把历史数据分为建模数据样本和检测数据样本,采用线性规划法求出参数的中心值和模糊幅度值。实验结果表明,该模型具有较高的精确度和可操作性。     

Some fixed point theorems in 1-M-complete fuzzy metric-like spaces

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept of fuzzy metric-like space and proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results.     

Stability of Cauchy–Jensen type functional equation in generalized fuzzy normed spaces

In this paper, we establish some stability results concerning the Cauchy–Jensen functional equation in generalized fuzzy normed spaces. The results of the present paper improve and extend some recent results.     

Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings

This paper generalizes a classical result about the space of bounded closed sets with the Hausdorff metric, and establishes the completeness of CB(X) with respect to the completeness of the metric space X, where CB(X) is the class of fuzzy sets with nonempty bounded closed α-cut sets, equipped with the supremum metric d_∞ which takes the supremum on the Hausdorff distances between the corresponding α-cut sets. In addition, some common fixed point theorems for fuzzy mappings are proved and two examples are given to illustrate the validity of the main results in fixed point theory.