Relaxed contractions in suprametric spaces: A unified framework with applications to nonlinear differential models

Büyükkaya A., Girgin E., Ahmad H., Younis M., Öztürk M.

AIMS Mathematics, cilt.11, sa.4, ss.9008-9040, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 4
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3934/math.2026372
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.9008-9040
  • Anahtar Kelimeler: boundary value problems, fixed-point theory, nonlinear operators, relaxed ϑ-contraction, suprametric space
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This paper develops a relaxed fixed-point framework for nonlinear operators acting on suprametric spaces. A new class of control functions ΘR is introduced, allowing strictly increasing but possibly discontinuous behaviors that go beyond the classical ϑ-contraction structure. Within this setting, several relaxed ϑR-type contractive conditions are formulated through max-based suprametric functionals and on complete suprametric spaces. These conditions guarantee the existence and uniqueness of fixed-points under a suitable jump requirement on the control function. The theory is supported by explicit examples showing how discontinuities and nonlinear growth patterns influence convergence. Finally, two differential models, namely a second-order particle motion problem and a fourth-order beam equation, are used to demonstrate that their associated integral operators admit unique solutions within the proposed relaxed suprametric framework.