# Richard's inequality, Cauchy-Schwarz's inequality and approximate solutions of Sincov's equation

## TL;DR

This paper explores the relationship between Richard's and Cauchy-Schwarz inequalities in inner product spaces and investigates the stability of Sincov's functional equation, showing that unbounded approximate solutions are exact.

## Contribution

It establishes a connection between classical inequalities and proves super-stability of Sincov's equation for unbounded functions.

## Key findings

- Unbounded approximate solutions to Sincov's equation are exact solutions.
- A link between Richard's inequality and Cauchy-Schwarz inequality is demonstrated.
- The super-stability of Sincov's equation is proven for unbounded mappings.

## Abstract

We observe a connection between Cauchy-Schwarz' and Richard's inequalities in inner product spaces and a Ulam-type stability problem for multiplicative Sincov's functional equation. We prove that this equation is super-stable for unbounded mappings, i.e. every unbounded approximate solution is an exact solution.