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arXiv · 2504.07546

Hyers-Ulam Type Stability of the Pexiderized Cauchy Functional Equation in Locally Convex Cones

Jafar Mohammadpour·Abbas Najati·Iz-iddine EL-Fassi
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Abstract

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.

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Jafar Mohammadpour, Abbas Najati, Iz-iddine EL-Fassi. 2025-04-10. Hyers-Ulam Type Stability of the Pexiderized Cauchy Functional Equation in Locally Convex Cones. https://arxiv.org/abs/2504.07546

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