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Some new Ostrowski type inequalities via Caputo \(k\)-fractional derivatives concerning \((n + 1)\)-differentiable generalized relative semi-\((r; m, p, q, h_1, h_2)\)-preinvex mappings. (English) Zbl 1430.26004

Summary: In this article, we first presented some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-\((r; m, p, q, h_1, h_2)\)-preinvex mappings. And then, a new identity concerning \((n+1)\)-differentiable mappings defined onm-invex set via Caputok-fractional derivatives is derived. By using the notion of generalized relative semi-\((r; m, p, q, h_1, h_2)\)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Ostrowski type inequalities via Caputo \(k\)-fractional derivatives are established. It is pointed out that some new special cases can be deduced from main results of the article.

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
26A33 Fractional derivatives and integrals
26D07 Inequalities involving other types of functions
26D10 Inequalities involving derivatives and differential and integral operators
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