and Applied Analysis 3 for some natural number n0. Moreover, if the second alternative holds, then i the sequence {Jnx} is convergent to a fixed point y∗ of J ; ii y∗ is the unique fixed point of J in the set Y : {y ∈ X | d J0x, y < ∞} and d y, y∗ ≤ 1/ 1 − L d y, Jy , for all , x, y ∈ Y . Following 30, 31 , we recall some basic facts concerning multi-normed spaces and some preliminary results. ...

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type f(x + y) + g(x − y) = h(x) + k(y), where f, g, h, k are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on f .

One might say that this formula allows one to solve the quadratic with a pencil. There is an analogous formula for the general quartic equation, ax+ bx + cx + dx+ e = 0. If you just have to know the formula or one way to derive it and don’t care about anything else, you may just skip to the last section of this paper. However, there is a mathematical notion of a pencil, which is rather cool and...

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation 3(f(x+ 2y) + f(x− 2y)) = 12(f(x + y) + f(x− y)) + 4f(3y)− 18f(2y) + 36f(y)− 18f(x).

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

The stability problem of functional equations originated from a question of Ulam 1 in 1940, concerning the stability of group homomorphisms. Let G1, · be a group and let G2, ∗ be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0, such that if a mapping h : G1 → G2 satisfies the inequality d h x · y , h x ∗ h y < δ for all x, y ∈ G1, then there exists a homomorphism H...

In this paper, we establish the general solution of the functional equation f(nx+ y) + f(nx− y) = nf(x+ y) + nf(x− y) + 2(f(nx)− nf(x))− 2(n − 1)f(y) for fixed integers n with n 6= 0,±1 and investigate the generalized Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

In this paper, we define the multicubic-quartic and multimixed cubic-quartic mappings characterize them. other words, unify system of functional equations defining a (resp., multicubic-quartic) mapping to single equation, namely, equation. We also show that under what conditions can be multicubic, multiquartic multicubic-quartic. Moreover, by using fixed point theorem, study generalized Hyers-U...