TY - JOUR
ID - 4951
TI - New estimates of Gauss-Jacobi and trapezium type inequalities for strongly $(h_{1},h_{2})$-preinvex mappings via general fractional integrals
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Kashuri, Artion
AU - Liko, Rozana
AU - Ali, Muhammad Aamir
AU - Budak, Huseyin
AD - Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, 9400, Vlora, Albania
AD - Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences,
Nanjing Normal University, 210023, China
AD - Department of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey
Y1 - 2021
PY - 2021
VL - 12
IS - 1
SP - 979
EP - 996
KW - Hermite-Hadamard inequality
KW - Holder inequality
KW - power mean inequality
KW - general fractional integrals
DO - 10.22075/ijnaa.2020.19718.2096
N2 - In this paper, authors discover two interesting identities regarding Gauss--Jacobi and trapezium type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss--Jacobi type integral inequalities for a new class of functions called strongly $(h_{1},h_{2})$--preinvex of order $\sigma>0$ with modulus $\mu>0$ via general fractional integrals are established. Also, using the second lemma, some new estimates with respect to trapezium type integral inequalities for strongly $(h_{1},h_{2})$--preinvex functions of order $\sigma>0$ with modulus $\mu>0$ via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different real numbers and new approximation error estimates for the trapezoidal are provided as well. These results give us the generalizations of some previous known results. The ideas and techniques of this paper may stimulate further research in the fascinating field of inequalities.
UR - https://ijnaa.semnan.ac.ir/article_4951.html
L1 - https://ijnaa.semnan.ac.ir/article_4951_44ccb936f00e77ef9a0a494cba86cb3e.pdf
ER -