Abstract
In this paper, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality and the Cauchy-Jensen additive functional inequality in matrix random normed spaces by using the fixed point method.
Highlights
1 Introduction The abstract characterization given for linear spaces of bounded Hilbert space operators in terms of matricially normed spaces [ ] implies that quotients, mapping spaces and various tensor products of operator spaces may again be regarded as operator spaces
We introduce the concept of matrix random normed space
In Section, we prove the Hyers-Ulam stability of the Cauchy-Jensen additive functional inequality ( . ) in matrix normed spaces by using the fixed point method
Summary
The abstract characterization given for linear spaces of bounded Hilbert space operators in terms of matricially normed spaces [ ] implies that quotients, mapping spaces and various tensor products of operator spaces may again be regarded as operator spaces. In , Isac and Rassias [ ] were the first to provide applications of stability theory of functional equations for the proof of new fixed point theorems with applications.
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