4 papers · 1 filter
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.…
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…