変数不等式による非線形問題のアルゴリズム

Huaping Huang¹, Imo Kalu Agwu², Umar Ishtiaq³

¹School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, China.

PloS one

|August 28, 2025

まとめ

この研究は,拡張的でない,厳格に擬約的マッピングのための共通の解決策を見つけるために,バナック空間における新しいマッピングを導入する. 固定点と変数不等式の問題の強力な収束定理を確立しています.

科学分野:

機能分析
非線形分析
オプティマイゼーション理論

背景:

固定点理論と変数不等式問題は,様々な数学分野において極めて重要です.
既存の方法は,特定の種類のマッピングとスペースでしばしば制限に直面します.
均等に凸で均等に滑らかなバナック空間は,これらの問題を解決するための堅固な枠組みを提供します.

研究の目的:

2つの均等に滑らかで均等に凸なバナック空間内の新しいマッピングを導入する.
強化された非拡張的および厳格な擬約的マッピングの固定点集合の共通の解決策を決定する.
関連変数不等式の問題の解のセットを確立する.

主な方法:

2つの均等に滑らかで均等に凸なバナック空間フレームワークを使用します.
収束分析のための新しいマッピングの開発と適用
マン・ハルパーンの反復的な方法を使う

主要な成果:

豊かな非拡張的および厳格な擬約的マッピングの有限なファミリーの固定点集合の共通解が得られた.
変数不等式の問題の解のセットを提供した.
マン・ハルパーン法を用いてこれらの解の集合に対する強力な収束定理を証明した.

結論:

導入されたマッピングとメソッドは,共通の解決策を見つけるのに重要な進歩をもたらします.
強力な収束定理は,文献にある既存の結果を一般化し,改善する.
この研究は,バナック空間における反復方法の理論的理解と実践的応用に貢献する.

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