Abstract
In this paper, we establish Hyers–Ulam–Rassias stability results belonging to two different set valued functional equations in several variables, namely additive and cubic. The results are obtained in the contexts of Banach spaces. The work is in the domain of set valued analysis.
Highlights
In this paper, we consider the stability properties of two set valued functional equations, one of which is additive and the other is cubic
The type of stability which we investigate here is Hyers–Ulam–Rassias stability
The basic notion of this stability can be illustrated by looking at the question on a linear equation: “Does an approximately linear equation have a linear approximation?" Today, it has many extended forms and has been studied in several domains of mathematics including differential equations [6], functional equations [7], isometries [8], etc
Summary
We consider the stability properties of two set valued functional equations, one of which is additive and the other is cubic. It may be mentioned that Hyers–Ulam–Rassias stability studied for set valued functional equations was initiated by Lu et al [9] and was followed in several works (e.g., [10,11,12,13,14,15]). Among different types of stabilities, the speciality of H–U–R stability is that when it occurs we have an assurance that we have an approximation to some desired degree of accuracy by the same type of mathematical concept. By this assurance, we can proceed with the same type of algorithms without any change
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