Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

Over the last few decades, a certain interesting class of functional equations were developed while obtaining generating functions many system distributions. This has numerous applications in modern disciplines such as wireless networks and communications. The Ulam stability theorem can be applied to investigating when approximated Banach spaces, algebra, so on. main focus this study is analyse relationship between equations, Hyers–Ulam–Rassias stability, space, quasi-beta normed fixed-point theory depth. significance work incorporation generalised additive equation space spaces by employing concrete techniques like direct methods. They are powerful tools for narrowing down mathematical models that describe wide range events. Some classes particular, have lately emerged from variety applications, Fourier transforms Laplace transforms. uses linear transformation explain our providing suitable examples.