Zulfiability: Convex-Like Functions under Zulfia Decomposition Mapping
Year: 2026
Type: article
Abstract: Convexity and invexity are classical convex-like structures based on directionalbehavior. Convexity uses the canonical direction x − u, while invexity replaces itwith a generalized mapping η(x, u).In this paper, we introduce Zulfia mappingZ(x, u) = η(x, u) + ∆(x, u),which decomposes generalized direction into directional and deviation components.We establish an Unavoidable Decomposition Theorem showing that any general-ized direction admits a direction–deviation representation. This provides a compactreference framework for Zulfia convexity and Zulfia invexity, with classical struc-tures recovered as limiting cases. We call these functions as Zulfiable functions orZulfiability.
Author: Khan, Zulfiqar Ali
Institution: Independent Research Association
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208770423
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