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Authors: ARTION KASHURI, ROZANA LIKO.
DOI: 10.24193/subbmath. 2021.3.02
Published Online: 2021-09-30
Published Print: 2021-09-30
pp. 423-440
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The authors have proved an identity for a generalized integral operator via differentiable function with parameters. By applying the established identity, the generalized trapezium, midpoint and Simpson type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means and new error estimates for the trapezium and midpoint quadrature formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.
Mathematics Subject Classification (2010): 26A51, 26A33, 26D07, 26D10, 26D15.
Keywords: Trapezium inequality, Simpson inequality, preinvexity, general fractional integrals.
