@article{Büyükkaya2026, 
author = {Abdurrahman Büyükkaya and Ekber Girgin and Haroon Ahmad and Mudasir Younis and Mahpeyker Öztürk},
title = {Relaxed contractions in suprametric spaces: A unified framework with applications to nonlinear differential models},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {9008-9040},
keywords = {suprametric space, relaxed ϑ-contraction, fixed-point theory, nonlinear operators, boundary value problems},
url = {https://www.sciopen.com/article/10.3934/math.2026372},
doi = {10.3934/math.2026372},
abstract = {This paper develops a relaxed fixed-point framework for nonlinear operators acting on suprametric spaces. A new class of control functions        Θ          R       is introduced, allowing strictly increasing but possibly discontinuous behaviors that go beyond the classical    ϑ-contraction structure. Within this setting, several relaxed        ϑ                  R            -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.}
}