Projection-constrained solvability for multivalued operator inclusions

Selah M.

APPLICABLE ANALYSIS, cilt.105, ss.1-18, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 105
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1080/00036811.2026.2737981
  • Dergi Adı: APPLICABLE ANALYSIS
  • Derginin Tarandığı İndeksler: Applied Science & Technology Source, Academic Search Ultimate (EBSCO), Scopus, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest), Aerospace Database, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1-18
  • 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 h ∈ Au + F(u),

where A is a bounded linear operator and F is a compact convexvalued

multivalued perturbation, and develop a nonlinear resolvent

framework based on the regularized operators Tα = α(I − π) + AA∗.

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.