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Measure Zero Stability Problem for Drygas Functional Equation with Complex Involution

In: Frontiers in Functional Equations and Analytic Inequalities

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ahmed Nuino & Muaadh Almahalebi & Ahmed Charifi, 2019. "Measure Zero Stability Problem for Drygas Functional Equation with Complex Involution," Springer Books, in: George A. Anastassiou & John Michael Rassias (ed.), Frontiers in Functional Equations and Analytic Inequalities, pages 183-193, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28950-8_11
    DOI: 10.1007/978-3-030-28950-8_11
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