8 papers · 1 filter
On the Fixed Point Property in Reflexive Banach Spaces
Faruk Alpay, Hamdi Alakkad
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach spac…
Quantization Errors, Human--AI Interaction, and Approximate Fixed Points in
Faruk Alpay, Hamdi Alakkad
We develop a rigorous measure-theoretic framework for the analysis of fixed points of nonexpansive maps in the space , with explicit consideration of quantization errors a…
New Approaches to the Fixed Point Property in L^1 Spaces
Faruk Alpay, Hamdi Alakkad
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, w…
The phi-Process: Operator-Algebraic Embeddings of Possibilities, Transfinite Stabilization, and a Quantitative Application to Sensory Depletion
Bugra Kilictas, Faruk Alpay
We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and or…
Anchored Implication & Event-Indexed Fixed Points in Hilbert Spaces: Uniqueness and Quantitative Rates
Faruk Alpay, Bugra Kilictas, Taylan Alpay
We develop a synthesis of orthomodular logic (projections as propositions) with operator fixed-point theory in Hilbert spaces. First, we introduce an anchored implication connectiv…
Logically Contractive Mappings: Fixed Points and Event-Indexed Rates
Faruk Alpay, Taylan Alpay
We introduce "logically contractive mappings" nonexpansive self-maps that contract along a subsequence of iterates and prove a fixed-point theorem that extends Banach's principle.…