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Journals / Hacettepe Journal of Mathematics and Statistics / 2024 / Volume: 53 Issue: 6

Introduction in third-order fuzzy differential subordination

Georgia Irina Oros(University of Oradea)0000-0003-2902-4455
Gheorghe Oros(University of Oradea)0000-0002-1000-094X
Özlem Güney(DICLE UNIVERSITY)0000-0002-3010-7795
Pages
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Publication Date
2024-12-28
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AI Summary & Key Takeaways

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

Several examples constructed as applications of the new results demonstrate the applicability of the new findings.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In light of the well-established and widely-used theory of differential subordination, recent works incorporating fuzzy elements into Geometric Function Theory have given rise to the concept of fuzzy differential subordination.
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Key Findings & Data:The research described in this paper aims to expand the concept of fuzzy differential subordination to third-order fuzzy differential subordination, building on an idea first put forth in 2011 by Jos\'{e} A.
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Conclusion & Impact:Several examples constructed as applications of the new results demonstrate the applicability of the new findings.
🔬Design:Research Article
📍Scope:2011 Verileri
⚙️Variables:third-order differential subordination · fuzzy differential subordination · admissible function

Abstract

In light of the well-established and widely-used theory of differential subordination, recent works incorporating fuzzy elements into Geometric Function Theory have given rise to the concept of fuzzy differential subordination. Second-order fuzzy differential subordinations were taken into consideration for studies up until this point. The research described in this paper aims to expand the concept of fuzzy differential subordination to third-order fuzzy differential subordination, building on an idea first put forth in 2011 by Jos\'{e} A. Antonino and Sanford S. Miller and still being investigated by scholars today. The key concepts and preliminary findings required for the development of this branch of fuzzy differential subordination are introduced. The class of admissible functions is specified, the fundamental theorems are established and the fundamental concepts of the third-order fuzzy subordination approach are presented. Several examples constructed as applications of the new results demonstrate the applicability of the new findings.

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Cite This Article

Oros, G. I., Oros, G., Güney, Ö. (2024). Introduction in third-order fuzzy differential subordination. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 6. https://doi.org/10.15672/hujms.1319541

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