Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 3
Submit an article Journal homepage
177
Views
47
CrossRef citations to date
0
Altmetric
Articles

Some k-fractional extensions of the trapezium inequalities through generalized relative semi-(m,h)-preinvexity

Tingsong Dua Department of Mathematics, College of Science, China Three Gorges University, Yichang, People's Republic of ChinaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-6072-1788View further author information
ORCID Icon,
Muhammad Uzair Awanb Department of Mathematics, Government College University, Faisalabad, PakistanView further author information
,
Artion Kashuric Department of Mathematics, Faculty of Technical Science, University ‘Ismail Qemali’, Vlora, AlbaniaView further author information
&
Shasha Zhaoa Department of Mathematics, College of Science, China Three Gorges University, Yichang, People's Republic of ChinaView further author information
Pages 642-662 | Received 01 Aug 2017, Accepted 03 May 2019, Published online: 14 May 2019

Citations (47)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (1)

Pei-Pei Wang, Ting Zhu & Ting-Song Du. (2021) Some inequalities using s-preinvexity via quantum calculus. Journal of Interdisciplinary Mathematics 24:3, pages 613-636.
Read now

Articles from other publishers (46)

Wenbing Sun & Haiyang Wan. (2024) New local fractional Hermite-Hadamard-type and Ostrowski-type inequalities with generalized Mittag-Leffler kernel for generalized h -preinvex functions . Demonstratio Mathematica 57:1.
Crossref
Nassima Nasri, Badreddine Meftah, Abdelkader Moumen & Hicham Saber. (2024) Fractional $ 3/8 $-Simpson type inequalities for differentiable convex functions. AIMS Mathematics 9:3, pages 5349-5375.
Crossref
Muhammad Bilal Khan, Jorge E. Macías-Díaz, Ali Althobaiti & Saad Althobaiti. (2023) Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels. Fractal and Fractional 7:7, pages 567.
Crossref
Taichun Zhou, Zhengrong Yuan & Tingsong Du. (2021) On the fractional integral inclusions having exponential kernels for interval-valued convex functions. Mathematical Sciences 17:2, pages 107-120.
Crossref
Miguel Vivas-Cortez, Maria Bibi, Muhammad Muddassar & Sa’ud Al-Sa’di. (2023) On local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) \left({\tilde{h}}_{1},{\tilde{h}}_{2}) -preinvexity involving local fractional integral operators with Mittag-Leffler kernel. Demonstratio Mathematica 56:1.
Crossref
Artion Kashuri, Soubhagya Kumar Sahoo, Munirah Aljuaid, Muhammad Tariq & Manuel De La Sen. (2023) Some New Hermite–Hadamard Type Inequalities Pertaining to Generalized Multiplicative Fractional Integrals. Symmetry 15:4, pages 868.
Crossref
Sa'ud Al‐Sa'di, Maria Bibi & Muhammad Muddassar. (2022) Some Hermite‐Hadamard's type local fractional integral inequalities for generalized γ‐preinvex function with applications. Mathematical Methods in the Applied Sciences 46:2, pages 2941-2954.
Crossref
WENBING SUN & HAIYANG WAN. (2023) HERMITE–HADAMARD-TYPE INEQUALITIES INVOLVING SEVERAL KINDS OF FRACTIONAL CALCULUS FOR HARMONICALLY CONVEX FUNCTIONS. Fractals 31:09.
Crossref
Yu Peng, Hao Fu & Tingsong Du. (2022) Estimations of Bounds on the Multiplicative Fractional Integral Inequalities Having Exponential Kernels. Communications in Mathematics and Statistics.
Crossref
Muhammad Aamir Ali, Hüseyin Budak, Mehmet Zeki Sarikaya & Erhan Set. (2022) Quantum ostrowski type inequalities for pre-invex functions. Mathematica Slovaca 72:6, pages 1489-1500.
Crossref
Hüseyin Budak, Seda Kılınç Yıldırım, Mehmet Zeki Sarıkaya & Hüseyin Yıldırım. (2022) Some parameterized Simpson-, midpoint- and trapezoid-type inequalities for generalized fractional integrals. Journal of Inequalities and Applications 2022:1.
Crossref
SHUHONG YU, TINGSONG DU & BO YU. (2022) PROPERTIES AND INTEGRAL INEQUALITIES INVOLVING WITH THE GENERALIZED s-TYPE PREINVEX MAPPINGS IN FRACTAL SPACE. Fractals 30:07.
Crossref
Muhammad Bilal Khan, Gustavo Santos-García, Muhammad Aslam Noor & Mohamed S. Soliman. (2022) Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities. Chaos, Solitons & Fractals 164, pages 112692.
Crossref
Muhammad Bilal Khan, Jorge E. Macías-Díaz, Savin Treanțǎ & Mohamed S. Soliman. (2022) Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions. Mathematics 10:20, pages 3851.
Crossref
Muhammad Bilal Khan, Adriana Cătaş & Omar Mutab Alsalami. (2022) Some New Estimates on Coordinates of Generalized Convex Interval-Valued Functions. Fractal and Fractional 6:8, pages 415.
Crossref
Yaoqun Wu. (2022) Hermite–Hadamard-Type Inequalities for h-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel. Fractal and Fractional 6:6, pages 309.
Crossref
SHUHONG YU, PSHTIWAN OTHMAN MOHAMMED, LEI XU & TINGSONG DU. (2022) AN IMPROVEMENT OF THE POWER-MEAN INTEGRAL INEQUALITY IN THE FRAME OF FRACTAL SPACE AND CERTAIN RELATED MIDPOINT-TYPE INTEGRAL INEQUALITIES. Fractals 30:04.
Crossref
Muhammad Bilal Khan, Jorge E. Macías-Díaz, Savin Treanțǎ, Mohammed S. Soliman & Hatim Ghazi Zaini. (2022) Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings. Fractal and Fractional 6:4, pages 178.
Crossref
Tingsong Du & Taichun Zhou. (2022) On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings. Chaos, Solitons & Fractals 156, pages 111846.
Crossref
Muhammad Bilal Khan, Hatim Ghazi Zaini, Jorge E. Macías-Díaz, Savin Treanțǎ & Mohamed S. Soliman. (2022) Some Fuzzy Riemann–Liouville Fractional Integral Inequalities for Preinvex Fuzzy Interval-Valued Functions. Symmetry 14:2, pages 313.
Crossref
Shuhong Yu & Tingsong Du. (2022) Certain inequalities in frame of the left-sided fractional integral operators having exponential kernels. AIMS Mathematics 7:3, pages 4094-4114.
Crossref
Muhammad LatifAmerAmer & Tingsong Du. (2022) Hermite-Hadamard type inequalities for harmonically-convex functions using fuzzy integrals. Filomat 36:12, pages 4099-4110.
Crossref
Bo Yu, Chun-Yan Luo & Ting-Song Du. (2021) On the refinements of some important inequalities via $(p,q)$-calculus and their applications. Journal of Inequalities and Applications 2021:1.
Crossref
WENBING SUN. (2021) HERMITE–HADAMARD TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES WITH MITTAG-LEFFLER KERNEL FOR GENERALIZED PREINVEX FUNCTIONS. Fractals 29:08.
Crossref
Muhammad Uzair Awan, Muhammad Zakria Javed, Michael Th. Rassias, Muhammad Aslam Noor & Khalida Inayat Noor. (2021) Simpson type inequalities and applications. The Journal of Analysis 29:4, pages 1403-1419.
Crossref
TINGSONG DU, CHUNYAN LUO & ZHIJIE CAO. (2021) ON THE BULLEN-TYPE INEQUALITIES VIA GENERALIZED FRACTIONAL INTEGRALS AND THEIR APPLICATIONS. Fractals 29:07.
Crossref
CHUNYAN LUO, YUPING YU & TINGSONG DU. (2021) AN IMPROVEMENT OF HÖLDER INTEGRAL INEQUALITY ON FRACTAL SETS AND SOME RELATED SIMPSON-LIKE INEQUALITIES. Fractals 29:05, pages 2150126.
Crossref
WENBING SUN. (2021) HERMITE–HADAMARD TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED s -PREINVEX FUNCTIONS AND THEIR GENERALIZATION . Fractals 29:04, pages 2150098.
Crossref
Saad Ihsan Butt, Saima Rashid, Muhammad Tariq & Miao-Kun Wang. (2021) Novel Refinements via –Polynomial Harmonically –Type Convex Functions and Application in Special Functions . Journal of Function Spaces 2021, pages 1-17.
Crossref
Jamshed Nasir, Shahid Qaisar, Saad Ihsan Butt, Hassen Aydi & Manuel De la Sen. (2021) Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications. AIMS Mathematics 7:3, pages 3418-3439.
Crossref
Muhammad Tariq, Soubhagya Kumar Sahoo, Fahd Jarad & Bibhakar Kodamasingh. (2021) Some integral inequalities for generalized preinvex functions with applications. AIMS Mathematics 6:12, pages 13907-13930.
Crossref
Wenbing Sun & Rui Xu. (2021) Some new Hermite-Hadamard type inequalities for generalized harmonically convex functions involving local fractional integrals. AIMS Mathematics 6:10, pages 10679-10695.
Crossref
Sevda Sezer. (2021) The Hermite-Hadamard inequality for $ s $-Convex functions in the third sense. AIMS Mathematics 6:7, pages 7719-7732.
Crossref
Hao Fu, Yu Peng & Tingsong Du. (2021) Some inequalities for multiplicative tempered fractional integrals involving the $ \lambda $-incomplete gamma functions. AIMS Mathematics 6:7, pages 7456-7478.
Crossref
Yuping Yu, Hui Lei, Gou Hu & Tingsong Du. (2021) Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings. AIMS Mathematics 6:4, pages 3525-3545.
Crossref
Shahid Mubeen, Rana Safdar Ali, Iqra Nayab, Gauhar Rahman, Kottakkaran Sooppy Nisar & Dumitru Baleanu. (2021) Some generalized fractional integral inequalities with nonsingular function as a kernel. AIMS Mathematics 6:4, pages 3352-3377.
Crossref
Wenbing Sun. (2020) Some Hermite–Hadamard type inequalities for generalized h-preinvex function via local fractional integrals and their applications. Advances in Difference Equations 2020:1.
Crossref
Saad Ihsan Butt, Artion Kashuri, Muhammad Nadeem, Adnan Aslam & Wei Gao. (2020) Approximately two-dimensional harmonic $(p_{1},h_{1})$-$(p_{2},h_{2})$-convex functions and related integral inequalities. Journal of Inequalities and Applications 2020:1.
Crossref
Tai-Chun Zhou, Zheng-Rong Yuan, Hong-Ying Yang & Ting-Song Du. (2020) Some parameterized inequalities by means of fractional integrals with exponential kernels and their applications. Journal of Inequalities and Applications 2020:1.
Crossref
Miguel Vivas-Cortez, Artion Kashuri & Jorge E. Hernández Hernández. (2020) Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions. Symmetry 12:6, pages 1034.
Crossref
Wenbing Sun & Qiong Liu. (2020) Hadamard type local fractional integral inequalities for generalized harmonically convex functions and applications. Mathematical Methods in the Applied Sciences 43:9, pages 5776-5787.
Crossref
Arshad Iqbal, Muhammad Adil Khan, Muhammad Suleman & Yu-Ming Chu. (2020) The right Riemann–Liouville fractional Hermite–Hadamard type inequalities derived from Green’s function. AIP Advances 10:4.
Crossref
Shahid Khan, Muhammad Adil Khan & Yu‐Ming Chu. (2019) Converses of the Jensen inequality derived from the Green functions with applications in information theory. Mathematical Methods in the Applied Sciences 43:5, pages 2577-2587.
Crossref
WENBING SUN. (2020) GENERALIZED h-CONVEXITY ON FRACTAL SETS AND SOME GENERALIZED HADAMARD-TYPE INEQUALITIES. Fractals 28:02, pages 2050021.
Crossref
Chunyan Luo, Hao Wang & Tingsong Du. (2020) Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications. Chaos, Solitons & Fractals 131, pages 109547.
Crossref
Jialu Nie, Jun Liu, Jiafeng Zhang & Tingsong Du. (2019) Estimation-type results on the k -fractional Simpson-type integral inequalities and applications . Journal of Taibah University for Science 13:1, pages 932-940.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.