Mixed Type Of Additive And Quintic Functional Equations

Abstract

In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form $$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$ in the set of real numbers.

Quattuortrigintic Functional Equation and its Hyers-Ulam Stability

“…In 1994, a generalization of Rassias theorem was obtained by Gâvruta [13] and this idea is known as generalized Hyers-Ulam-Rassias stability. After that, the general stability problems of various functional equations such as additive [23,24], quadratic [22,28], cubic [5,21,29,30], quartic [5,33], quintic and sextic [4,25,32], septic and octic [47], nonic [6,42], decic [3], undecic [40], quattuordecic [41], hexadecic [18], octadecic [26], vigintic [39], viginticduo [17], quattuorvigintic [27,38,35] and trigintic [8] and so on.…”

Euler-Lagrange radical functional equations with solution and stability

“…In 2015, Abasalt Bodaghi et al [2] analyzed the general solution and stability of a mixed type of quintic-additive functional equation of the form…”

Functional equation and its modular stability with and without Δp-condition

“…For the detailed study on Ulam problem and its recent developments called generalized Hyers-Ulam-Rassias stability, one can refer [1,8,11]. In 1950, Nakano [7] established the modular linear spaces and further developed by many authors, one can refer [5,6,9].…”

“…In 2015, Abasalt Bodaghi et al [1] investigated the stabilities of following mixed type equation h(3y + z) − 5h(2y + z) + h(2y − z) + 10h(y + z) − 5h(y − z) = 10h(z) + 4h(2y) − 8h(y) for all y, z ∈ R.…”