Abstract:Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^{*}$. We introduce a hybrid projection method for approximating a common element of four classes of constraints: the set of fixed points of a countable family of generalized nonexpansive-type maps, the solution sets of countably many equilibrium problems, the solution sets of countably many variational inequality problems, and the zero sets of countably many maximal monotone operators. The algorithm combines equilibrium resolvents, variational inequality resolvents, generalized resolvents of maximal monotone operators and a shrinking projection step. Under precise monotonicity, continuity and closedness assumptions, we prove that the generated sequence converges strongly to the generalized projection of the initial point onto the common solution set. We also establish residual convergence, derive convex minimization consequences, present a finite-truncation result, and give an illustrative Hilbert-space specialization showing why the countable setting cannot, in general, be reduced to a finite-family theorem.
From: Markjoe Uba Ph.D. [view email]
[v1]
Sat, 30 May 2026 06:54:54 UTC (14 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。