Kashuri, Artion, Liko, Rozana, Ali, Muhammad, Budak, Huseyin. (1400). New estimates of Gauss-Jacobi and trapezium type inequalities for strongly $(h_{1},h_{2})$-preinvex mappings via general fractional integrals. هنرهای کاربردی, 12(1), 979-996. doi: 10.22075/ijnaa.2020.19718.2096
Artion Kashuri; Rozana Liko; Muhammad Aamir Ali; Huseyin Budak. "New estimates of Gauss-Jacobi and trapezium type inequalities for strongly $(h_{1},h_{2})$-preinvex mappings via general fractional integrals". هنرهای کاربردی, 12, 1, 1400, 979-996. doi: 10.22075/ijnaa.2020.19718.2096
Kashuri, Artion, Liko, Rozana, Ali, Muhammad, Budak, Huseyin. (1400). 'New estimates of Gauss-Jacobi and trapezium type inequalities for strongly $(h_{1},h_{2})$-preinvex mappings via general fractional integrals', هنرهای کاربردی, 12(1), pp. 979-996. doi: 10.22075/ijnaa.2020.19718.2096
Kashuri, Artion, Liko, Rozana, Ali, Muhammad, Budak, Huseyin. New estimates of Gauss-Jacobi and trapezium type inequalities for strongly $(h_{1},h_{2})$-preinvex mappings via general fractional integrals. هنرهای کاربردی, 1400; 12(1): 979-996. doi: 10.22075/ijnaa.2020.19718.2096

New estimates of Gauss-Jacobi and trapezium type inequalities for strongly $(h_{1},h_{2})$-preinvex mappings via general fractional integrals

International Journal of Nonlinear Analysis and Applications
مقاله 79، دوره 12، شماره 1، مرداد 2021، صفحه 979-996    اصل مقاله (483.58 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.19718.2096
نویسندگان
Artion Kashuri* 1؛ Rozana Liko1؛ Muhammad Aamir Ali2؛ Huseyin Budak3
1Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, 9400, Vlora, Albania
2Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, 210023, China
3Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey
چکیده
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.
کلیدواژه‌ها
Hermite-Hadamard inequality؛ Holder inequality؛ power mean inequality؛ general fractional integrals
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