Iterative Procedures and Continuous-Time Systems for Variational Inclusions via Graph Convergence of \(\phi\)-Accretive Mappings
Fixed Point Methods and Optimization, Volume 3, Issue 2, August 2026, Pages 114–129
MOHD. FALAHAT KHAN
Department of Mathematics, Aligarh Muslim University, Aligarh, U. P., India
SYED SHAKAIB IRFAN
Department of Mathematics, Aligarh Muslim University, Aligarh, U. P., India
IQBAL AHMAD
Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi Arabia
MOHD. SHARIQUE
Department of Mathematics, Aligarh Muslim University, Aligarh, U. P., India
Abstract
This manuscript develops the notion of graph convergence for \(\Phi\)-accretive mappings in \(p\)-uniformly smooth Banach spaces, proving its equivalence with convergence of associated resolvent and Cayley mappings. A perturbed iterative procedure is then proposed for solving variational inclusions governed by such mappings. Under suitable hypotheses, we establish both solution existence and convergence of the generated sequence, complemented by an investigation of a generalized resolvent-driven continuous-time system that elucidates trajectory behavior and equilibrium stability. Computational experiments confirm the theoretical predictions and demonstrate practical applicability.
Cite this Article as
Mohd. Falahat Khan, Syed Shakaib Irfan, Iqbal Ahmad, and Mohd. Sharique, Iterative Procedures and Continuous-Time Systems for Variational Inclusions via Graph Convergence of $\phi$-Accretive Mappings, Fixed Point Methods and Optimization, 3(2), 114–129, 2026