Measure Zero Stability Problem for Drygas Functional Equation with Complex Involution

Ahmed Nuino (), Muaadh Almahalebi () and Ahmed Charifi ()
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Ahmed Nuino: University of Ibn Tofail, Department of Mathematics, Faculty of Sciences
Muaadh Almahalebi: University of Ibn Tofail, Department of Mathematics, Faculty of Sciences
Ahmed Charifi: University of Ibn Tofail, Department of Mathematics, Faculty of Sciences

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 183-193 from Springer

Abstract: Abstract In this chapter, we discuss the Hyers–Ulam stability theorem for the σ-Drygas functional equation f ( x + y ) + f ( x + σ ( y ) ) = 2 f ( x ) + f ( y ) + f ( σ ( y ) ) $$\displaystyle f(x+y)+f\big (x+\sigma (y)\big )=2f(x)+f(y)+f\big (\sigma (y)\big ) $$ for all ( x , y ) ∈ Ω ⊂ ℂ 2 $$(x,y)\in \varOmega \subset \mathbb {C}^{2}$$ for Lebesgue measure m(Ω) = 0, where f : ℂ → Y $$f:\mathbb {C}\to Y$$ and σ : X → X is an involution.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28950-8_11

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DOI: 10.1007/978-3-030-28950-8_11

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