Simpson’s type inequalities for strongly ( s , m )-convex functions in the second sense and applications

Abstract

Some new inequalities of Simpson's type for functions whose third derivatives in absolute value at some powers are strongly (s, m)convex in the second sense are provided. An application to the Simpson's quadrature rule is also provided.

Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives

“…In recent years, inequality theory attracts many researchers due to its applications in our daily life and within the mathematics [1][2][3][4][5][6][7][8][9]. Let 0 < x 1 ≤ x 2 ≤ • • • ≤ x n and let μ � (μ 1 , μ 2 , .…”

Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation

“…Given M, set the system precision at d2:2Me. Given M and the system precision, calculate the weights w i , 1 ≤ i ≤ 2M, using (22). Then, given the transform b ζðsÞ and the argument 3 Journal of Function Spaces…”

“…Due to the wide range of applications, FIDEs have attracted researchers. Therefore, a large number of analytic and numerical methods have been developed for finding the solutions of FIDEs [22][23][24][25][26]. For example, the authors [27] utilized the fractional differential transform method for the solution of fractional integrodifferential equations.…”

Simpson’s type inequalities for η-convex functions via k-Riemann–Liouville fractional integrals

“…Many authors have studied and provided several generalizations of this inequality over the years. For some results related to the Simpson's inequality, we refer the interested reader to the papers [1,2,5,9,10,[15][16][17].…”