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<p>The foundation of locally convex cone theory relies on order-theoretic concepts that induce specific topological frameworks. Within this structure, cones naturally possess three distinct topologies: lower, upper, and symmetric. In this paper, we consider the Hyers-Ulam type stability of the Pexiderized Cauchy functional equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f(x+y)=g(x)+h(y)\)</EquationSource> </InlineEquation> in locally convex cones. Additionally, we present several significant corollaries that follow from our primary findings.</p>

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Hyers-ulam type stability of the Pexiderized Cauchy functional equation in locally convex cones

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Jafar Mohammadpour,
  • Abbas Najati,
  • Iz-iddine EL-Fassi

摘要

The foundation of locally convex cone theory relies on order-theoretic concepts that induce specific topological frameworks. Within this structure, cones naturally possess three distinct topologies: lower, upper, and symmetric. In this paper, we consider the Hyers-Ulam type stability of the Pexiderized Cauchy functional equation \(f(x+y)=g(x)+h(y)\) in locally convex cones. Additionally, we present several significant corollaries that follow from our primary findings.