Manuscript Topics

Variational inequality theory and fixed point theory constitute two fundamental pillars of nonlinear analysis and optimization, with deep theoretical foundations and wideranging applications in mathematics, engineering, economics, and applied sciences. Over the past decades, these theories have experienced rapid development, driven by advances in functional analysis, convex analysis, operator theory, and numerical algorithms.

Variational inequalities provide a unified framework for studying equilibrium problems, optimization problems, and constrained nonlinear systems, while fixed point theory offers powerful tools for analyzing existence, uniqueness, and convergence properties of solutions to nonlinear equations and inclusions. The interaction between these two areas has led to significant progress in algorithmic design, convergence analysis, and applications to real-world models.

The aim of this special issue is to present recent advances in variational inequality problems and fixed point theory, including new theoretical results, innovative numerical methods, and emerging applications. The issue seeks to provide a forum for researchers to exchange ideas, highlight current trends, and stimulate further developments in these closely related fields.

This special issue welcomes high-quality original research articles as well as authoritative survey papers. Contributions may address theoretical, computational, or applied aspects of variational inequalities and fixed point methods.

Key Topics:

Potential topics include but are not limited to the following:  
• Variational inequality problems in Hilbert and Banach spaces  
• Fixed point theory for nonlinear mappings and multivalued operators  
• Monotone, pseudomonotone, and accretive operators  
• Projection, extragradient, Tseng-type, and inertial algorithms  
• Splitting methods and operator-splitting techniques  
• Convergence analysis and complexity of iterative methods  
• Variational inclusions and equilibrium problems  
• Quasi-variational and hemivariational inequalities  
• Fixed point methods on metric spaces and manifolds  
• Applications to optimization, game theory, signal processing, and image analysis  
• Numerical methods and computational aspects of variational inequalities  
• Stability and sensitivity analysis of solution sets

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