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- Nicole Brillouët-Belluot, Janusz Brzdȩk, Krzysztof Ciepliński
- 2014

and Applied Analysis 3 We can describe that latter result saying that the Cauchy functional equation 2.8 is HyersUlam stable (or has the Hyers-Ulam stability) in the class of functions Y . For examples of various possible definitions of stability for functional equations and some discussions on them we refer to 9 . The result of Hyers was extended by Aoki… (More)

The fixed point method, which is the second most popular technique of proving the Hyers–Ulam stability of functional equations, was used for the first time in 1991 by J.A. Baker who applied a variant of Banach’s fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow Radu’s approach and make… (More)

- Janusz Brzdek, Krzysztof Cieplinski
- Applied Mathematics and Computation
- 2012

- Krzysztof Cieplinski
- Computers & Mathematics with Applications
- 2011

We show that if F :S1 → S1 is a homeomorphism of the unit circle S1 and the rotation number α(F ) of F is irrational, then the Schröder equation Φ ( F(z) = e2πiα(F Φ(z), z ∈ S1, has a unique (up to a multiplicative constant) continuous at a point of the limit set of F solution. We apply this result to prove that if F is a non-trivial continuous and disjoint… (More)

We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into n-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and p-adic numbers, which are the most important examples of non-Archimedean fields,… (More)

- Anna Bahyrycz, Krzysztof Cieplinski, Jolanta Olko
- Applied Mathematics and Computation
- 2015

Let I a, b , J c, d be closed, bounded, and nondegenerate i.e., neither of them consists of a single point real intervals, and let f : I → I, F : J → J be continuous functions. The aim of this paper is to discuss, under some additional assumptions on the maps f and F, the problem of topological conjugacy of f and F. More precisely, we investigate the… (More)

- Krzysztof Cieplinski
- Appl. Math. Lett.
- 2011

- Krzysztof Cieplinski
- Appl. Math. Lett.
- 2010

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