5 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 ar…
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…
Transfinite Iteration of Operator Transforms and Spectral Projections in Hilbert and Banach Spaces
Faruk Alpay, Taylan Alpay, Hamdi Alakkad
We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For norm…
Transfinite Operator Fixed Points on Hilbert Spaces: An Alpay Algebra Approach
Faruk Alpay, Hamdi Alakkad, Taylan Alpay
This work develops a functional-analytic framework based on the transfinite iteration of a self-adjoint operator. Beginning with a densely defined self-adjoint operator on a Hi…