ABSTRACT
This research proposes a framework for fixed point index formulas in nonconvex conical regions with boundary curvature constraints, aiming to extend Krasnosel’ski˘ ı fixed point theorem and related index theories.
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Key findings
Proposes extension of Krasnosel’ski˘ ı fixed point theorem to nonconvex conical shells.
Introduces curvature-regularized retractions and computable index formulas.
Combines topological degree theory with geometric measure-theoretic tools.
Limitations & open questions
Does not explicitly address practical computational aspects or specific applications beyond theoretical development.