The study of fixed points on the maps fulfilling certain contraction requirements has several applications and been focus numerous research endeavors. On other hand, as an extension idea best approximation, proximity point (ƁƤƤ) emerges. approximation theorem ensures existence approximate solution; is considered for addressing problem in order to arrive at optimum solution. This paper introduce...

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

In this paper, we obtain a characterization of linear spaces which may be normed so as to become complete, linear, normed metric spaces. In this connection, K. Kunugui and M. Fréchet have shown that every metric space S is isometric with a subset of a complete, linear, normed metric space. I t follows from our result that if the cardinal number of 5 is the limit of a denumerable sequence of car...

In this paper, we generalize the Mazur–Ulam theorem in the fuzzy real n-normed strictly convex spaces. Mathematics Subject Classification. Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

In this paper, we establish the Mazur–Ulam theorem in the fuzzy strictly convex real normed spaces. Mathematics Subject Classification. Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

In this paper, we investigate the general solution and the generalized Hyers-Ulam stability of a new functional equation satisfied by $f(x) = x^{24}$, which is called quattuorvigintic functional equation in intuitionistic fuzzy normed spaces by using the fixed point method.These results can be regarded as an important extension of stability results corresponding to functional equations on norme...

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability o...

In this paper, λI-statistical convergence is defined to generalize statistical on Neutrosophic normed spaces. As it known, theory, which brings a new breath daily life and complex scientific studies we encounter with many uncertainties, rapidly developing field study subjects. Thus, researchers show great interest in philosophical approach try transfer related topics quickly. For purpose, study...

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

P.Kostyrko et al [10] introduced the concept of Iconvergence of sequence in metric space and studied some properties of such convergence. Since then many author have been studied these subject and obtained various results [29,30,31,32,?] Note that I-convergence is an interesting generalization of statistical convergence. The concept of 2-normed space was initially introduced by Gähler [7] as an...