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Some Different Type Integral Inequalities and Their Applications

In: Mathematical Analysis and Applications

Author

Listed:
  • Artion Kashuri

    (University Ismail Qemali of Vlora)

  • Rozana Liko

    (University Ismail Qemali of Vlora)

Abstract

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized-m- ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ -convex mappings. Secondly, an identity pertaining twice differentiable mappings defined on m-invex set is used. By using the notion of generalized-m- ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ -convexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard, Ostrowski, and Simpson type inequalities via fractional integrals are established. It is pointed out that some new special cases can be deduced from main results. At the end, some applications to special means for different positive real numbers are provided as well.

Suggested Citation

  • Artion Kashuri & Rozana Liko, 2019. "Some Different Type Integral Inequalities and Their Applications," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Mathematical Analysis and Applications, pages 287-317, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-31339-5_10
    DOI: 10.1007/978-3-030-31339-5_10
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