In this paper, we give a general solution of a refined quadratic functional equation and then investigate its generalized Hyers–Ulam stability in quasi-normed spaces and in non-Archimedean normed spaces. AMS Subject Classification: 39B82, 39B62

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...

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

In this paper we prove result for Jensen type mapping in the setting of intuitionistic fuzzy normed spaces. We generalize a Hyers-Ulam stability result in the framework of classical normed spaces.

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fix...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

1. Basic definitions 2. Riesz’ Lemma 3. Counter-examples for unique norm-minimizing element 4. Normed spaces of continuous linear maps 5. Dual spaces of normed spaces 6. Baire’s theorem 7. Banach-Steinhaus/uniform-boundedness theorem 8. Open mapping theorem 9. Closed graph theorem 10. Hahn-Banach theorem Many natural spaces of functions, such as C(K) for K compact, and C[a, b], have natural str...

We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...

The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilis...