Different type parameterized inequalities for preinvex functions with respect to another function via generalized fractional integral operators and their applications
UDC 517.5The authors have proved an identity with two parameters for differentiable function with respect to another function via generalized integral operator. By applying the established identity, the generalized trapezium, midpoint and Simpson type integral inequalities have been discovered. It i...
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| Date: | 2021 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/805 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5The authors have proved an identity with two parameters for differentiable function with respect to another function via generalized integral operator. 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.
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| DOI: | 10.37863/umzh.v73i9.805 |