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- Title
Some Classical Inequalities Associated with Generic Identity and Applications.
- Authors
Javed, Muhammad Zakria; Awan, Muhammad Uzair; Bin-Mohsin, Bandar; Budak, Hüseyin; Dragomir, Silvestru Sever
- Abstract
In 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 γ and parameter ξ.
- Subjects
CONVEX functions; DIFFERENTIABLE functions; SPECIAL functions; INTEGRAL inequalities; EXPLANATION
- Publication
Axioms (2075-1680), 2024, Vol 13, Issue 8, p533
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms13080533