Startseite On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions
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On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions

  • Artion Kashuri ORCID logo EMAIL logo und Rozana Liko ORCID logo
Veröffentlicht/Copyright: 21. Mai 2019

Abstract

In the present paper, a new class of generalized beta (r,g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss–Jacobi type quadrature formula involving generalized beta (r,g)-preinvex functions are given. Moreover, some generalizations of Hermite–Hadamard type inequalities for generalized beta (r,g)-preinvex functions that are twice differentiable via k-fractional integrals are established. These general inequalities give us some new estimates for Hermite–Hadamard type k-fractional integral inequalities and also extend some results appeared in the literature; see [A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s,m,φ)-preinvex functions, Aust. J. Math. Anal. Appl. 13 2016, 1, Article ID 16]. At the end, some applications to special means are given.

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Received: 2017-03-25
Accepted: 2019-02-02
Published Online: 2019-05-21
Published in Print: 2019-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 21.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jaa-2019-0007/html
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