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Impact of Fixed Point Theory on Ulam-Hyers Stability in Normed Spaces

In: Functional Equations and Ulam’s Problem

Author

Listed:
  • Erdal Karapınar

    (Atilim University, Department of Mathematics
    China Medical University Hospital, China Medical University, Department of Medical Research)

  • Marija Cvetković

    (Faculty of Sciences and Mathematics, University of Niš, Department of Mathematics)

  • Seher Sultan Yeşilkaya

    (Tokat Gaziosmanpaşa University, Department of Mathematics Education)

Abstract

Fixed point theorems have been used extensively in solving Ulam-Hyers stability problems. In this chapter we will focus on Ulam-Hyers stability of different types of functional equations in normed spaces, their modifications and generalizations like β $$\beta $$ -normed spaces, p-normed spaces, non-Archimedean normed space, fuzzy and random normed spaces. We collect the new results on this topic with following fixed point theorems that were used in their acquiring. Wide range of approaches to the proof of some well-known stability results is also presented from the angle of Fixed Point Theory.

Suggested Citation

  • Erdal Karapınar & Marija Cvetković & Seher Sultan Yeşilkaya, 2026. "Impact of Fixed Point Theory on Ulam-Hyers Stability in Normed Spaces," Springer Books, in: Themistocles M. Rassias (ed.), Functional Equations and Ulam’s Problem, pages 189-265, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-08949-6_11
    DOI: 10.1007/978-3-032-08949-6_11
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