Research Information System
AIMS Mathematics, vol.11, no.4, pp.9008-9040, 2026 (SCI-Expanded, Scopus)
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.