Javed, Muhammad ZakriaAwan, Muhammad UzairBin-Mohsin, BandarBudak, HuseyinDragomir, Silvestru Sever2025-10-112025-10-1120242075-1680https://doi.org/10.3390/axioms13080533https://hdl.handle.net/20.500.12684/21587In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski's inequality, trapezoidal inequality, midpoint inequality, Simpson's inequality, Newton-type inequalities, and several two-point open trapezoidal inequalities. Also, we provide the numerical and visual explanation of our principal findings. Later, we provide some novel applications to the theory of means, special functions, error bounds of composite quadrature schemes, and parametric iterative schemes to find the roots of linear functions. Also, we attain several already known and new bounds for different values of gamma and parameter xi.en10.3390/axioms13080533info:eu-repo/semantics/openAccessconvex functioninequalitytrapezoidalmidpointSimpsonNewtonquadrature schemesArticle138WOS:001305851200001Q2