Integral inequalities are very useful in finding the error bounds for numerical integration formulas. In this paper, we prove some multiplicative integral first-time differentiable s-convex functions. These new help different formulas calculus. The use of function extends results convex functions and covers a large class functions, which is main motivation using s-convexity. To inequalities, derive two identities setting Then, with these identities, Simpson Ostrowski types generalized...

ABSTRACT In mathematical analysis and optimization, studying inequalities is crucial in advancing theoretical practical applications. This paper delves into the intricate world of Weddle's type inequalities, specifically focusing on coordinated convex functions. Following a comprehensive study understanding, this article establishes new for A identity functions introduced. Utilizing newly established identity, error bounds rule two variables are proved. The results advance understanding...

In numerical analysis, the quadrature formulas serve as a pivotal tool for approximating definite integrals. this paper, we introduce family of and analyze their associated error bounds convex functions. The main advantage these new is that from bounds, can find different formulas. This work extends traditional such midpoint formula, trapezoidal Simpson's Boole's formula. We also use power mean Hölder's integral inequalities to more general sharp bounds. Furthermore, give example...

This paper presents a rigorous proof of novel multiplicative integral identity and utilize it to establish new Boole's type inequalities for multiplicatively convex functions. These newly established can be helpful in finding the bounds formula within framework calculus. Moreover, provide best optimal approximations polynomials degree six. Finding an error term using first derivative is excellent achievement inequality theory because class first-time differentiable functions more extensive...

This paper establishes some new inequalities of Hermite–Hadamard–Mercer type for [Formula: see text]-convex functions in the framework text]-calculus and classical calculus. Some text]-midpoint-Mercer text]-differentiable are also proved. Moreover, computational analysis newly established convex given to prove that bounds this better than those existing ones. It is shown with mathematical examples valid text]-calculus.

<title>Abstract</title> In this article, we give Jensen Mercer Inequality for interval-valuedco-ordinated convex functions because inequality was a challenging problem forresearchers working in the field of inequalities and set valued functions. By use new inequality, establish Hermite--Hadamard-Mercer type These newly established forinterval-valued are generalization existing Hermite-Hadamardinequalities. Moreover, numericalexamples to check validity results. The results ofthe study shows...

Abstract In this paper, authors establish a new identity for differentiable function using generic integral operators. By applying it, some inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications found.