Projection-constrained solvability for multivalued operator inclusions
Applicable Analysis, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1080/00036811.2026.2737981
- Dergi Adı: Applicable Analysis
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Finite-approximate solvability, multivalued operator inclusions, nonlinear resolvent methods, projection-constrained solvability
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
In this paper, we introduce the notion of finite-approximate solvability for multivalued operator inclusions in Hilbert spaces. We study projection-constrained inclusions of the form (Formula presented.) where A is a bounded linear operator and F is a compact convex-valued multivalued perturbation, and develop a nonlinear resolvent framework based on the regularized operators (Formula presented.). Using multivalued fixed-point techniques, we establish existence of nonlinear resolvent selections and derive sufficient and necessary residual conditions for finite-approximate solvability. We also show that finite-rank projection geometry, compactness, convexity, and orthogonality assumptions are essential for the solvability mechanism, and develop Galerkin-type approximation schemes for recovering solvability asymptotically. The obtained results extend finite-approximate solvability theory from single-valued operator equations to nonlinear multivalued inclusions.