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This Special Issue of the journal Axioms pays tribute to Professor Hong-Kun Xu's significant contributions and details recent important advances in theory, methods, and applications of nonlinear analysis, optimization theory, fixed point theory, and algorithms for nonlinear problems. It comprises original, creative, and high-quality research papers that inspire advances in fixed point, coincidence point, and best proximity point theory, set-valued analysis, nonlinear and variational methods for ODEs and PDEs, non-smooth analysis and optimization, inverse and ill-posed problems, convex analysis, matrix theory, and their applications.

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