in  this paper, we investigate the generalizedhyers-ulam-rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{z}-{0,pm1}$) in $p-$banach spaces.

and Applied Analysis 3 It follows from 2.1 and 2.6 that 2f ( x y 2 ) − g x − h(y) 2f ( x y 2 ) − g(y z) − h x − z − [ 2f (x z 2 ) − g 2z − h x − z ] [ 2f ( y 2z 2 ) − g 2z − h(y) ] − [ 2f ( y 2z 2 ) − g(y z) − h z ] [ 2f (x z 2 ) − g x − h z ] ∈ 3V − 2V 2.7 for all x, y ∈ X with ‖x‖ ‖y‖ < d. Hence, by 2.1 and 2.7 , we have 2f ( x y 2 ) − g x − h(y) ∈ 3V − 2V 2.8 for all x, y ∈ X. Letting x 0 y ...

Let X, Y be complex vector spaces. It is shown that if a mapping f : X → Y satisfies f (x + iy) + f (x− iy) = 2f (x) − 2f (y) (0.1) or f (x + iy) − f (ix + y) = 2f (x) − 2f (y) (0.2) for all x, y ∈ X , then the mapping f : X → Y satisfies f (x + y) + f (x− y) = 2f (x) + 2f (y) for all x, y ∈ X . Furthermore, we prove the generalized Hyers-Ulam stability of the functional equations (0.1) and (0....

Sarcopenia and cachexia present characteristic features of a decrease in skeletal muscle mass and strength, anorexia, and lack of motivation. Treatments for these diseases have not yet been established, although selective androgen receptor modulators (SARMs) are considered as therapeutic targets. We previously reported that a novel SARM compound, SARM-2f, exhibits anabolic effect on muscles, wi...

There is much evidence that in human immunodeficiency virus type 1 (HIV-1)-infected individuals, strong cytotoxic T lymphocyte (CTL)-mediated immune pressure results in the selection of HIV-1 mutants that have escaped from wild-type-specific CTLs. If escape mutant-specific CTLs are not elicited in new hosts sharing donor HLA molecules, the transmission of these mutants results in the accumulati...

In  this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.

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.