On the stability of radical septic functional equations

Abstract

This paper deals with the approximate solution of the following functional equation fx7+y77=f(x)+f(y), where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi-β-Banach spaces and (β,p)-Banach spaces. We also prove the nonstability of the previous functional equation in a relevant case.

Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces

“…Consider that Q 2 : E → F is an another Euler-Lagrange quadratic function which satisfying (10). Hence, by φ(θv 1 ) = θ 2 φ(v 1 ) (by Theorem 2) and ( 10), (7), it follows that…”

“…Rassias [4] proposed an extension of the Hyers Theorem in 1978, allowing for an unbounded Cauchy difference. A number of authors have examined and generalized stability problems of various functional equations that have been discussed in different normed spaces by using a fixed-point approach over the last few decades (see [5][6][7][8][9][10][11][12]).…”

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

“…Modern mathematicians state that an equation is stable within a specific type of function if every function in that category that significantly fulfils the equation is close to the optimal solution of the equation. Mathematicians have investigated quite a number of stability problems with diverse functional equations (radical, reciprocal, logarithmic, and algebraic) in recent times [4][5][6][7][8].…”

Existence and nonexistence of positive solutions for the second-order m-point eigenvalue impulsive boundary value problem

“…Many of the mathematical problems encountered in the study of impulsive differential equations cannot be treated with the usual techniques within the standard framework of ordinary differential equations. For the introduction of the basic theory of impulsive equations, see [3,5,6,15,21], and the papers [2,4,8,[11][12][13][14][24][25][26][27].…”