Stability Estimates for an Arithmetic Functional Equation with Brzdȩk Fixed Point Approaches

Heejeong Koh ()
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Heejeong Koh: College of Liberal Arts, Dankook University, 152, Jukjeon, Suji, Yongin 16890, Gyeonggi, Republic of Korea

Mathematics, 2023, vol. 11, issue 7, 1-10

Abstract: We introduce an arithmetic functional equation f ( x 2 + y 2 ) = f ( x 2 ) + f ( y 2 ) and then investigate stability estimates of the functional equation by using the Brzdȩk fixed point theorem on a non-Archimedean fuzzy metric space and a non-Archimedean fuzzy normed space. To apply the Brzdȩk fixed point theorem, the proof uses the linear relationship between two variables, x and y .

Keywords: stability; arithmetic functional equation; fixed point; Brzd?k fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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