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...

in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...

In this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers– Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.

In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real ...

In this paper, we consider the problem of farthest poinst for bounded sets in a real 2-normed spaces. We investigate some properties of farthest points in the setting of 2-normalised spaces and present various characterizations of b-farthest point of elements by bounded sets in terms of b-linear functional. We also provide some applications of farthest points in the setting of 2inner product sp...

in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

the main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. we develop the theory of t-bestsimultaneous approximation in quotient spaces. then, we discuss the relationshipin t-proximinality and t-chebyshevity of a given space and its quotientspace.

In this paper we introduce and investigate I2-convergence, I∗ 2 -convergence, I2-limit points, and I2-cluster points of a double sequence in a fuzzy 2-normed linear space. We prove a decomposition theorem for I2-convergence of double sequences. The notions of I2-double Cauchy and I∗ 2 -double Cauchy sequence are defined, and some of their properties are studied.

In this paper, we consider the problem of the farthest poinst for bounded sets in a real 2-normed spaces. We investigate some properties of farthest points in the setting of 2-normalised spaces and present various characterizations of b-farthest point of elements by bounded sets in terms of b-linear functional. We also provide some applications of farthest points in the setting of 2inner produc...