Abstract
In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann–Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.
Highlights
One of the most important inequalities for bounded functions is the Ostrowski inequality which gives an estimate for the deviation of the values of a smooth function from its mean value
This paper aims to establish some trapezoid and Ostrowski-type inequalities for functions of bounded variations with two variables via generalized fractional integrals
We present several trapezoid and Ostrowski-type inequalities for functions of bounded variation with two variables via generalized fractional integrals
Summary
One of the most important inequalities for bounded functions is the Ostrowski inequality which gives an estimate for the deviation of the values of a smooth function from its mean value. Some papers were devoted to study on Ostrowski-type inequalities for other kinds of convexities [3,4,5,6]. Set first proved the fractional version of Ostrowski inequality for s-convex functions via Riemann–. Many studies were devoted to new versions of Ostrowski-type inequalities for functions of bounded variation. This paper aims to establish some trapezoid and Ostrowski-type inequalities for functions of bounded variations with two variables via generalized fractional integrals. Trapezoidand Ostrowski-type inequalities for functions of bounded variations with two variables are established in Sections 4 and 5, respectively.
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