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In this paper, we derive some error estimates of Simpson's second type quadrature formula for functions of bounded variation and Lipschitzian mappings. Also, similar error estimations for absolutely continuous functions whose first derivatives belong to Lp[γ, δ] with (p < 1 ≤ ∞) are established. Finally, with the help of the results given in this work, some Simpson's type inequalities involving special means are presented. [ABSTRACT FROM AUTHOR]

This study seeks to derive novel quantum variations of Simpson's inequality by primarily utilizing the convexity characteristics of functions. Additionally, the study examines the credibility of the obtained results through the presentation of relevant numerical examples and graphs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study some new classes of convex functions which are called generalized harmonic convex and generalized harmonic log-convex functions. These new classes of harmonic functions unify serval new and previous known classes of harmonic convex functions. We derive some estimates for the class of functions whose certain powers of the absolute value are generalized harmonic convex function. Results obtained in this paper continue to hold for several classes of harmonic convex functions, which can be viewed as special cases. The ideas and techniques of this may inspire research in this field. [ABSTRACT FROM AUTHOR]

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In this paper, we introduce a new class of harmonic preinvex functions, which are called harmonic h-preinvex functions. Several new Ostrowski-type inequal- ities for harmonic h-preinvex functions via Riemann-Liouville fractional integrals are established. Some special cases are also discussed, which appears to be new ones. The results obtained in this paper continue to hold for these cases. Interested readers are encouraged to find the applications of the harmonic h-preinvex functions in pure and applied sciences. This is an interesting topic for future research. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce a new class of convex functions with respect to non-negative functions h and bifunction n(., .), which is called generalized (p, r, h, n-convex functions. We derive some new integral inequalities for this class of functions. Some special cases are also discussed. The ideas and techniques of this paper may stimulate further research. [ABSTRACT FROM AUTHOR]

In the paper, we use an auxiliary result to derive some new integral inequalities for n-times differentiable harmonic convex functions. Some special cases are are also investigated. Results obtained in this paper can be viewed as significant development in integral inequality theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of relative harmonic m-convex functions with respect to an arbitrary non-negative function. New integral inequalities are obtained via the relative harmonic m-convex functions. Some special cases are considered which can be obtained from our main results. The ideas and technique of this paper motivate further research in this fascinating are. [ABSTRACT FROM AUTHOR]