Some Hermite-Hadamard Type Inequalities via Katugampola Fractional for pq-Convex on the Interval-Valued Coordinates
Main Article Content
Abstract
In this paper, we established the Hermite-Hadamard inequalities via Katugampola fractional. Meanwhile, interval analysis is a particular case of set-interval analysis. We established the fractional inequalities and these results are an extension of a previous research.
Article Details
References
- H.Y. Budak, C.C. Bilişik, A. Kashuri and M.A. Ali, Hermite-Hadamard Type Inequalities For The Interval-Valued Harmonically h-Convex Functions Via Fractional Integrals, Appl. Math. E-Notes, 21 (2021), 12-32. https://www.emis.de/journals/AMEN/2021/AMEN-200121.pdf.
- H. Chen, U.N. Katugampola, Hermite–hadamard and Hermite–hadamard–fejér Type Inequalities for Generalized Fractional Integrals, J. Math. Anal. Appl. 446 (2017), 1274–1291. https://doi.org/10.1016/j.jmaa.2016.09.018.
- T. M. Costa, Jensen’s Inequality Type Integral for Fuzzy-Interval-Valued Functions, Fuzzy Sets Syst. 327 (2017), 31–47. https://doi.org/10.1016/j.fss.2017.02.001.
- T.M. Costa, H. Román-Flores, Some Integral Inequalities for Fuzzy-Interval-Valued Functions, Inform. Sci. 420 (2017), 110–125. https://doi.org/10.1016/j.ins.2017.08.055.
- Z.B.Fang, R. Shi, On the (p, h)-Convex Function and Some Integral Inequalities, J. Inequal. Appl. 2014 (2014), 45. https://doi.org/10.1186/1029-242X-2014-45.
- Y. Guo, G. Ye, D. Zhao, W. Liu, Some Integral Inequalities for Log-h-Convex Interval-Valued Functions, IEEE Access. 7 (2019), 86739–86745. https://doi.org/10.1109/access.2019.2925153.
- G. Hu, H. Lei, T. Du, Some Parameterized Integral Inequalities for p-Convex Mappings via the Right Katugampola Fractional Integrals, AIMS Math. 5 (2020), 1425–1445. https://doi.org/10.3934/math.2020098.
- M.B. Khan, M.A. Noor, K.I. Noor, Y.M. Chu, New Hermite-Hadamard-Type Inequalities for (h1, h2)-Convex FuzzyInterval-Valued Functions, Adv. Differ. Equ. 2021 (2021), 149. https://doi.org/10.1186/s13662-021-03245-8.
- H. Kara, M.A. Ali, H. Budak, Hermite-hadamard-type Inequalities for Interval-valued Coordinated Convex Functions Involving Generalized Fractional Integrals, Math. Meth. Appl. Sci. 44 (2020), 104–123. https://doi.org/10.1002/mma.6712.
- U.N. Katugampola, New Approach to a Generalized Fractional Integral, Appl. Math. Comput. 218 (2011), 860–865. https://doi.org/10.1016/j.amc.2011.03.062.
- U.N. Katugampola, New Approach to a Generalized Fractional Derivatives, Bull. Math. Anal. Appl. 6 (2014), 1-15.
- U.N. Katugampola, Mellin Transforms of Generalized Fractional Integrals and Derivatives, Appl. Math. Comput. 257 (2015), 566–580. https://doi.org/10.1016/j.amc.2014.12.067.
- Z. Li, Kamran, M.S. Zahoor, H. Akhtar, Hermite–Hadamard and Fractional Integral Inequalities for Interval-Valued Generalized p-Convex Function, J. Math. 2020 (2020), 4606439. https://doi.org/10.1155/2020/4606439.
- X. Liu, G. Ye, D. Zhao, W. Liu, Fractional Hermite–hadamard Type Inequalities for Interval-Valued Functions, J Inequal Appl. 2019 (2019), 266. https://doi.org/10.1186/s13660-019-2217-1.
- F.-C. Mitroi, K. Nikodem, S. Wąsowicz, Hermite–hadamard Inequalities for Convex Set-Valued Functions, Demonstr. Math. 46 (2013), 655-662. https://doi.org/10.1515/dema-2013-0483.
- R.E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliff, 1966.
- R.E. Moore, R.B. Kearfott, M.J. Cloud, Introduction to Interval Analysis, SIAM, Philadelphia, 2009.
- M. Noor Aslam, M. Awan Uzair, K. Noor Inayat, Integral Inequalities for Two-Dimensional pq-Convex Functions, Filomat. 30 (2016), 343–351. https://doi.org/10.2298/fil1602343n.
- M.A. Noor, K.I. Noor, S. Iftikhar, Nonconvex Functions and Integral Inequalities, Punjab Univ. J. Math. 47 (2015), 19-27.
- M.A. Noor, K.I. Noor, M.V. Mihai, M.U. Awan, Hermite-Hadamard Inequalities for Differentiable p-Convex Functions Using Hypergeometric Functions, Researchgate. (2015), https://doi.org/10.13140/RG.2.1.2485.0648.
- R. Osuna-Gómez, M.D. Jiménez-Gamero, Y. Chalco-Cano, M.A. Rojas-Medar, Hadamard and Jensen Inequalities for s-Convex Fuzzy Processes, in: Soft Methodology and Random Information Systems, Springer Berlin Heidelberg, Berlin, Heidelberg, 2004: pp. 645–652. https://doi.org/10.1007/978-3-540-44465-7_80.
- E. Sadowska, Hadamard Inequality and a Refinement of Jensen Inequality for Set—Valued Functions, Results. Math. 32 (1997), 332–337. https://doi.org/10.1007/bf03322144.
- E. Set, İ. Mumcu, Hermite–Hadamard-Type Inequalities for F -Convex Functions via Katugampola Fractional Integral, Math. Probl. Eng. 2021 (2021), 5549258. https://doi.org/10.1155/2021/5549258.
- E. Set and A. Karaoğlan, Hermite-Hadamard and Hermite-Hadamard-Fejér Type Inequalities for (k, h)-Convex Function via Katugampola Fractional Integrals, Konuralp J. Math. 5 (2017), 181-191. https://dergipark.org.tr/en/download/article-file/351071.
- F. Shi, G. Ye, D. Zhao, W. Liu, Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions, Mathematics. 8 (2020), 534. https://doi.org/10.3390/math8040534.
- F. Shi, G. Ye, D. Zhao, W. Liu, Some Fractional Hermite–hadamard-Type Inequalities for Interval-Valued Coordinated Functions, Adv. Differ. Equ. 2021 (2021), 32. https://doi.org/10.1186/s13662-020-03200-z.
- T. Toplu, E. Set, İ. İşcan, S. Maden, Hermite-Hadamard Type Inequalities for p-Convex Functions via Katugampola Fractional Integrals, Facta Univ., Ser.: Math. Inform. 34 (2019) 149-164. https://doi.org/10.22190/fumi1901149t.
- H. Yaldiz, A.O. Akdemir, Katugampola Fractional Integrals Within the Class of Convex Functions, Turk. J. Sci. III (2018), 40-50.
- Y. Yu, H. Lei, G. Hu, T. Du, Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and p-convex mappings, AIMS Math. 6 (2021), 3525–3545. https://doi.org/10.3934/math.2021210.
- D. Zhao, M.A. Ali, G. Murtaza, Z. Zhang, On the Hermite–hadamard Inequalities for Interval-Valued Coordinated Convex Functions, Adv. Differ. Equ. 2020 (2020), 570. https://doi.org/10.1186/s13662-020-03028-7.
- D. Zhao, T. An, G. Ye, W. Liu, New Jensen and Hermite–hadamard Type Inequalities for h-Convex Interval-Valued Functions, J. Inequal. Appl. 2018 (2018), 302. https://doi.org/10.1186/s13660-018-1896-3.