Random Normed Spaces Research Articles

THE RANDOM OF LACUNARY STATISTICAL ON χ^2 OVER p− METRIC SPACES DEFINED BY MUSIELAK

Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. Recently Mohiuddine and Aiyup defined the notion of lacunary statistical convergence and lacunary statistical Cauchy in random 2-normed spaces. In this paper, we define and study the notion of lacunary statistical convergence and lacunary of statistical Cauchy sequences in random on χ 2 over p− metric spaces defined by Musielak and prove some theorems which generalizes Mohiuddine and Aiyup results.

Approximation on the reciprocal functional equation in several variables in matrix non-Archimedean random normed spaces

In this paper, we investigate the generalized Hyers-Ulam stability of a reciprocal type functional equation in several variables in matrix non-Archimedean random normed spaces by direct and fixed point methods.

Stability of Pexiderized Quadratic Functional Equation in Random 2-Normed Spaces

The aim of this paper is to investigate the stability of Hyers-Ulam-Rassias type theorems by considering the pexiderized quadratic functional equation in the setting of random 2-normed spaces (RTNS), while the concept of random 2-normed space has been recently studied by Goleţ (2005).

On $\Lambda$-statistical convergence of order $\alpha$ in random 2-normed space

On $\Lambda$-statistical convergence of order $\alpha$ in random 2-normed space

ON DIFFERENCE IDEAL CONVERGENCE OF DOUBLE SEQUENCES IN RANDOM 2-NORMED SPACES

An ideal I is a family of subsets of positive integers ℕ which is closed under taking finite unions and subsets of its elements. We define and study the notions of Δn-ideal convergence and Δn-ideal Cauchy double sequences in random 2-normed spaces and prove some interesting theorems.

RN HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS: A DIRECT METHOD

In this paper we prove Hyres-Ulam-Rassias stability of an additive functional equation in random normed spaces. The concept of Hyers-Ulam- Rassias stability originated from Th.M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.

DIRECT METHOD AND RN-APPROXIMATELY FUNCTIONAL EQUATIONS

In this paper, we prove the generalized Hyers-Ulam stability of an additive functional equation in random normed spaces.

On \(\nabla\)-statistical convergence in random 2-normed space

Recently in [19], Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of \(\nabla\)-statistical convergence and \(\nabla
 \)-statistical Cauchy sequences by using \(\lambda\)-sequences in random 2-normed spaces and we prove some theorems.

Stability of Functional Equations in Matrix Random Normed Spaces: A Fixed Point Approach

In this paper, we prove the Hyers–Ulam stability of the Cauchy additive functional equation and the quadratic functional equation in matrix random normed spaces by using fixed point method.

On the Stability of Cubic and Quadratic Mapping in Random Normed Spaces under ArbitraryT-Norms

We prove the stability of some functional equations in the random normed spaces under arbitraryt-norms.

Stability of a mixed type additive and quartic functional equation

In this paper we obtain the general solution of a mixed additive and quartic functional equation. We also prove the Hyers-Ulam stability of this functional equation in random normed spaces.

Stability of a quadratic and additive type functional equation in random normed spaces

Stability of a quadratic and additive type functional equation in random normed spaces

Stability of functional inequalities in matrix random normed spaces

In this paper, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality and the Cauchy-Jensen additive functional inequality in matrix random normed spaces by using the fixed point method.

ℐ𝒦-Convergence in the Topology Induced by Random 2-Normed Spaces

We study ℐ𝒦-convergence which is common generalization of the ℐ*-convergence of sequences in the topology induced by random 2-normed spaces and prove some important results.

Lacunary Statistical Limit Points in Random 2-Normed Spaces

We introduce the notionθ-cluster points, investigate the relation betweenθ-cluster points and limit points of sequences in the topology induced by random 2-normed spaces, and prove some important results.

On the stability of the n-dimensional quadratic and additive functional equation in random normed spaces via fixed point method

On the stability of the n-dimensional quadratic and additive functional equation in random normed spaces via fixed point method

A Minimax Theorem forL-0-Valued Functions on Random Normed Modules

We generalize the well-known minimax theorems toL¯0-valued functions on random normed modules. We first give some basic properties of anL0-valued lower semicontinuous function on a random normed module under the two kinds of topologies, namely, the (ε,λ)-topology and the locallyL0-convex topology. Then, we introduce the definition of random saddle points. Conditions for anL0-valued function to have a random saddle point are given. The most greatest difference between our results and the classical minimax theorems is that we have to overcome the difficulty resulted from the lack of the condition of compactness. Finally, we, using relations between the two kinds of topologies, establish the minimax theorem ofL¯0-valued functions in the framework of random normed modules and random conjugate spaces.

On a problem of Schwaiger in random normed spaces

We consider a problem of Schwaiger in the setting of random normed spaces to obtain a characterization for the completeness of these spaces by means of the stability of the Cauchy additive functional equation.

Lacunary generalized difference statistical convergence in random 2-normed spaces

Recently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary An-statistical convergence and lacunary An-statistical Cauchy sequences in random 2-normed spaces using la-cunary density and prove some interesting theorems.

On generalized double statistical convergence in a random 2-normed space

Recently, the concept of statistical convergence has been studied in 2-normed and random 2-normed spaces by various authors. In this paper, we shall introduce the concept of λ-double statistical convergence and λ-double statistical Cauchy in a random 2-normed space. We also shall prove some new results. MSC: 40A05; 40B50; 46A19; 46A45