Sabit Nokta Özelliğinin Sağlanamamasını Belirlemeye Yönelik Asimptotik ve Fonksiyonel Çerçeveler: AI–c₀, N₁ ve Fonksiyonel Sandviç Özelliği

Öz

Banach uzaylarında Sabit Nokta Özelliği’nin (FPP) başarısızlığını saptamak için kullanılan analitik ve geometrik araçları iyileştirip geliştiriyoruz. Klasik belirleyiciler arasında, Dowling–Lennard–Turett tarafından ortaya konan asimptotik olarak izometrik c_0 kopyaları (AI-c_0) ile Álvaro–Cembranos–Mendoza’nın analitik N_1özelliği yer alır. Álvaro–Cembranos–Mendoza’nın önemli sonuçlarından birisi AI-c_0 ⇒ N_1 geçerli iken tersi doğru değildir; dolayısıyla N_1 özelliğine sahip olup, asimptotik olarak izometrik bir c_0 kopya içermeyen uzaylar mevcuttur. Bu gerçekten daha güçlü bir sonuç elde etmek üzerine, hem geometrik bir AI-c_0 kopyasının bulunmadığı hem de klasik N_1kestiriminin yetersiz kaldığı sınıflarda dahi FPP başarısızlığını yakalamayı sürdüren “üstten baskın” (sup-dominated) ve “fonksiyonel sandviç” (FSP, sFSP) çerçevelerini tanıtıyoruz. Yapıların ima yönlerini, örnekler, karşı-örnekler ve Hahn–Banach temelli kurulumlarla birlikte şekiller ve karşılaştırmalı tablolar sunuyoruz.

Anahtar Kelimeler

• Sabit nokta özelliği
• genişlemeyen fonksiyon
• asimptotik izometrik kopya
• N_1 özelliği

New Asymptotic and Functional Properties for Detecting the Failure of the Fixed Point Property: A Unified Framework Beyond Classical c_0 and N_1 Structures

Öz

We refine analytic and geometric tools for detecting the failure of the Fixed Point Property (FPP) in Banach spaces. Classical detectors include asymptotically isometric copies of c_0 (AI-c_0), due to Dowling-Lennard-Turett, and the analytic N_1 property of Álvaro–Cembranos–Mendoza. Importantly, AI-c_0 implies N_1, while the converse fails; thus there exist spaces with N_1 but without any asymptotically isometric copy of c_0. Building on these, we introduce sup-dominated and functional-sandwiched frameworks (FSP, sFSP) that still detect FPP failure in classes where both a geometric AI-c_0 copy is absent and the classical N_1 estimate is too weak. We provide implications, examples, counterexamples, and Hahn-Banach based constructions, together with figures and comparative tables.

Anahtar Kelimeler

• Fixed point property
• nonexpansive mappings
• asymptotically isometric copy
• N_1 property

Kaynakça

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