Abstract
The investigation of the stabilities of various types of equations is an interesting and evolving research area in the field of mathematical analysis. Recently, there are many research papers published on this topic, especially additive, quadratic, cubic, and mixed type functional equations. We propose a new functional equation in this study which is quite different from the functional equations already dealt in the literature. The main feature of the equation dealt in this study is that it has three different solutions, namely, additive, quadratic, and mixed type functions. We also prove that the stability results hold good for this equation in intuitionistic random normed space (briefly, IRN-space).
Highlights
The theory of random normed spaces (RN-spaces) is important as a generalization of the deterministic result of linear normed spaces and in the study of random operator equations
Aoki generalized the result of Hyers [3] for approximate additive mappings and by Rassias [4] for approximate linear mappings by allowing the difference Cauchy equation k f ðx + yÞ − f ðxÞ − f ðyÞk to be controlled by εð∥x∥p+∥y∥pÞ
Shu et al [33,34,35] discussed various differential equations to study the HyersUlam stability, which provides a wide view of this stability problem
Summary
The theory of random normed spaces (RN-spaces) is important as a generalization of the deterministic result of linear normed spaces and in the study of random operator equations. Shu et al [33,34,35] discussed various differential equations to study the HyersUlam stability, which provides a wide view of this stability problem In this present work, we introduce a new mixed type additive-quadratic functional equation. A new mixed additive-quadratic functional equation is proposed in this paper, and its stability results are proved in an intuitionistic random normed space. This type of functional equation can be of use in solving many physical problems and has significant relevance in various scientific fields of research and study. Providing a wealth of essential insights and new concepts in the field of functional equations
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