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

Erdal Karapınar, Marija Cvetković () and Seher Sultan Yeşilkaya ()
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Erdal Karapınar: Atilim University, Department of Mathematics
Marija Cvetković: Faculty of Sciences and Mathematics, University of Niš, Department of Mathematics
Seher Sultan Yeşilkaya: Tokat Gaziosmanpaşa University, Department of Mathematics Education

A chapter in Functional Equations and Ulam’s Problem, 2026, pp 189-265 from Springer

Abstract: 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.

Keywords: Ulam-Hyers stability; Fixed point theory; Normed spaces; Non-Archimedean normed spaces; Random normed spaces; Fuzzy normed spaces; 47H10; 39B82 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-08949-6_11

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DOI: 10.1007/978-3-032-08949-6_11

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