in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

In the present paper, we study frames for finite-dimensional vector spaces over an arbitrary field. We develop a theory of dual in order to obtain and different representations elements space provided by frame. relate introduced with classical one Hilbert apply it three types spaces: conjugate closed subfields complex numbers (in particular, cyclotomic fields), metric spaces, ultrametric normed...

The aim of this paper is to introduce the concepts of compatible mappings and compatible mappings of type (R) in non-Archimedean Menger probabilistic normed spaces and to study the existence problems of common fixed points for compatible mappings of type (R), also, we give an applications by using the main theorems.

In this paper, we prove the generalized Hyres–Ulam–Rassias stability of the mixed type cubic and quartic functional equation f (x + 2y) + f (x − 2y) = 4(f (x + y) + f (x − y)) − 24f (y) − 6f (x) + 3f (2y) in non-Archimedean ℓ-fuzzy normed spaces.

In this paper, we prove the stability of the functional equation ∑ 1 i, j n,i = j ( f (xi + x j)+ f (xi − x j) ) = (n−1) n ∑ i=1 ( 3 f (xi)+ f (−xi) ) in non-Archimedean normed spaces. Mathematics subject classification (2010): 39B82, 46S10, 39B52.

In this paper, we investigate the generalized Hyers–Ulam stability for the functional equation f(ax+y)+af(y−x)− a(a+ 1) 2 f(x)− a(a+ 1) 2 f(−x)− (a+1)f(y) = 0 in non-Archimedean normed spaces. Mathematics Subject Classification: 39B52, 39B82

In this paper, we obtain the general solution and investigate the Hyers-Ulam-Rassias stability of the functional equation f(ax− y)± af(x± y) = (a± 1)[af(x)± f(y)] in non-Archimedean -fuzzy normed spaces. Mathematics Subject Classification: 39B55, 39B52, 39B82

In this paper, we introduce some new classes of proximal contraction mappings and establish  best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...