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

Authors : Veysel Nezir

Pages : 38-46

Doi:10.58688/kujs.1820324

View : 39 | Download : 61

Publication Date : 2025-12-26

Article Type : Research Paper

Abstract :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.
Keywords : Sabit nokta özelliği, genişlemeyen fonksiyon, asimptotik izometrik kopya, N_1 özelliği

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