Fixed Points and Generalized Hyers‐Ulam Stability | Zendy

Liviu Cădariu | Zendy; Laura Găvruţa | Zendy; P. Găvruţa | Zendy

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Fixed Points and Generalized Hyers‐Ulam Stability

Author(s) -

Liviu Cădariu,

Laura Găvruţa,

P. Găvruţa

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/712743

Subject(s) - mathematics , fixed point theorem , fixed point , stability (learning theory) , class (philosophy) , variable (mathematics) , point (geometry) , pure mathematics , discrete mathematics , mathematical analysis , geometry , artificial intelligence , machine learning , computer science

In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions. Also, we show that some recent fixed-points results in Brzdęk et al., (2011) and Brzdęk and Ciepliński (2011) can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzdęk and Ciepliński (2011) is given. Several corollaries, obtained directly from our main result, show that this is a useful tool for proving properties of generalized Hyers-Ulam stability for some functional equations in a single variable

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