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

• Autorzy: Kashuri Artion , Liko Rozana

Identyfikatory

DOI

10.1515/jaa-2019-0007

• Języki publikacji: EN

Abstrakty

EN

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), no. 1, Article ID 16]. At the end, some applications to special means are given.

Słowa kluczowe

EN

Hermite-Hadamard type inequality; Hölder's inequality; Minkowski's inequality; power mean inequality; Riemann-Liouville fractional integral; s-convex functions in the second sense; m-invex; P-function

PL

nierówność typu Hermite'a-Hadamarda; nierówność Höldera; nierówność Minkowskiego; nierówność między średnimi uogólnionymi; całkowanie ułamkowe Riemanna-Liouville'a; funkcje s-wypukłe

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2019
• Tom: Vol. 25, nr 1
• Strony: 59--72
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Kashuri Artion

• Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania

autor

Liko Rozana

• Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).