A New Class of (α,η,(Q,h),L)-Contractions in Triple Controlled Metric-Type Spaces with Application to Polynomial Sine-Type Equations

This paper introduces a novel class of generalized contractions, termed (α,η,(Q,h),L)-contraction mapping, within the context of triple controlled metric-type spaces, extending the framework of fixed point theory in controlled structures. The proposed mapping is defined using α-admissible and η-subadmissible functions, in conjunction with a control pair (Q,h) of upper class of type I, and incorporates Wardowski’s function L-contraction condition. Under suitable hypotheses, we establish both the existence and uniqueness of fixed points for this class of mappings. Several corollaries are derived as special cases of the main result. Moreover, we provide a nontrivial application by analyzing the solvability of a nonlinear equation involving powers of the sine function, thereby illustrating the utility of the developed theory.