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The stability of a Cosine-Sine Functional Equation on abelian groups

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Ajebbar Omar, Elqorachi Elhoucien, Themistocles M. Rassias

Commutative Algebra · Submitted 24 Oct 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.

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arXiv ID1810.10295 (version 1)
Pith ID2WANBHZU, Pith's permanent record of this paper and its review
CitationAjebbar Omar, Elqorachi Elhoucien, Themistocles M. Rassias. "The stability of a Cosine-Sine Functional Equation on abelian groups." arXiv:1810.10295 (2018). https://pith.science/paper/2WANBHZU
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,673 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.04 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group. contribution 0.73 0.95 0.95 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.

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