in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced...

In this article, we define a new non-archimedean metric structure, called cophenetic metric, on persistent homology classes of all degrees. We then show that zeroth together with the and hierarchical clustering algorithms number different metrics do deliver statistically verifiable commensurate topological information based experimental results obtained datasets. also observe resulting clusters...

The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metr...

The aim of this paper is to generalize the results of Ahmad, Ashraf and Rhoades [1] in the setting of 2 Non Archimedean Menger PM-space introduced by Renu Chugh and Sumitra [2]. In fact, 2 nonArchimedean Menger PM-space (briefly 2 N. A. Menger PM-space ) is the generalization of 2-metric space in probabilistic setting, i.e., the case where instead of the distances between two or more points one...

In the paper [7] C. Huang and C. Moraga suggested a new method to extract fuzzy if-then rules from training data based on information matrix technique with Gaussian membership function. In this paper, we extend this method to the Archimedean t-normed space of quasitriangular fuzzy numbers.

The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric space using general contractive condition of integral type, without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorems, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy...