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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2022 / Volume: 71 Issue: 4

An overview to analyticity of dual functions

Olgun Durmaz(ATATURK UNIVERSITY)0000-0002-0913-3307
Buşra Aktaş(KIRIKKALE UNIVERSITY)0000-0002-1285-7250
Osman Keçilioğlu(KIRIKKALE UNIVERSITY)0000-0002-5149-5221
Pages
—
Publication Date
2022-12-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, the equivalent of the inverse function theorem in dual space is given by a theorem and proved.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the analyticity conditions of dual functions are clearly examined and the properties of the concept derivative are given in detail.
📊
Key Findings & Data:Then, using the dual order relation, the dual analytic regions of dual analytic functions are constructed such that a collection of these regions forms a basis on $D^n$.
💡
Conclusion & Impact:Finally, the equivalent of the inverse function theorem in dual space is given by a theorem and proved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dual numbers · topology · dual analytic functions

Abstract

In this paper, the analyticity conditions of dual functions are clearly examined and the properties of the concept derivative are given in detail. Then, using the dual order relation, the dual analytic regions of dual analytic functions are constructed such that a collection of these regions forms a basis on $D^n$. Finally, the equivalent of the inverse function theorem in dual space is given by a theorem and proved.

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Cite This Article

Durmaz, O., Aktaş, B., Keçilioğlu, O. (2022). An overview to analyticity of dual functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 4. https://doi.org/10.31801/cfsuasmas.1035344

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