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Fixed Points and Generalized Hyers‐Ulam Stability

Author

Listed:
  • L. Cădariu
  • L. Găvruţa
  • P. Găvruţa

Abstract

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.

Suggested Citation

  • L. Cădariu & L. Găvruţa & P. Găvruţa, 2012. "Fixed Points and Generalized Hyers‐Ulam Stability," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:712743
    DOI: 10.1155/2012/712743
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    References listed on IDEAS

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    1. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, January.
    2. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
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