A Generalized Direction-Correction Framework for Coupled Mappings
Year: 2026
Type: article
Abstract: We develop a generalized mathematical framework for mappings that combine directionaland correction components and allow their coupled extension. The basic structure is thedirection–correction decompositionZ(x, u) = η(x, u) + ∆(x, u),where η(x, u) represents a directional component and ∆(x, u) represents a correction com-ponent. Two such mappings are then coupled through an interaction operator, producingZC = Z1 + Z2 + C(Z1, Z2).The framework separates combined direction, combined correction, and interaction into dis-tinct mathematical components. Fundamental properties, balance relations, limiting cases,and illustrative coupling structures are developed. A scalar bilinear interaction demonstrateshow non-additive terms arise. The formulation is intended as a mathematical foundation forsubsequent developments in optimization, game theory, quantum theory, physics, statistics,and related fields.
Author: Khan, Zulfiqar Ali
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214528895
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