Midpoint inequalities via strong convexity using positive weighted symmetry kernels. (English) Zbl 1479.52017
The classical midpoint inequalities for strongly convex functions are generalized for weighted fractional integral settings, extending various results from the literature.
Reviewer: Sorin-Mihai Grad (Paris)
MSC:
| 52A41 | Convex functions and convex programs in convex geometry |
| 26B25 | Convexity of real functions of several variables, generalizations |
References:
| [1] | Liu, W.; Wen, W.; Park, J., Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals, Journal of Nonlinear Sciences and Applications, 9, 3, 766-777 (2016) · Zbl 1329.26014 · doi:10.22436/jnsa.009.03.05 |
| [2] | Han, J.; Mohammed, P. O.; Zeng, H., Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function, Open Mathematics, 18, 1, 794-806 (2020) · Zbl 1482.26030 · doi:10.1515/math-2020-0038 |
| [3] | Awan, M. U.; Noor, M. A.; Noor, K. I., Hermite-Hadamard Inequalities for Exponentially Convex Functions, Applied Mathematics & Information Sciences, 12, 2, 405-409 (2018) · doi:10.18576/amis/120215 |
| [4] | Rashid, S.; Ashraf, R.; Aslam Noor, M.; Inayat Noor, K.; Chu, Y. M., New weighted generalizations for differentiable exponentially convex mapping with application, AIMS Mathematics, 5, 4, 3525-3546 (2020) · Zbl 1484.26037 · doi:10.3934/math.2020229 |
| [5] | Saleem, M. S.; Chu, Y. M.; Jahangir, N.; Akhtar, H.; Jung, C. Y., On Generalized Strongly \(p\)-Convex Functions of Higher Order, Journal of Mathematics, 2020 (2020) · Zbl 1489.26048 · doi:10.1155/2020/8381431 |
| [6] | Tunc, M.; Subas, Y.; Karabayir, I., On some Hadamard type inequalities for MT- Convex Functions, International Journal of Open Problems in Computer Science and Mathematics, 6, 2, 102-113 (2013) · doi:10.12816/0006173 |
| [7] | Sarikaya, M. Z., On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, 25, 2, 134-147 (2014) · Zbl 1284.26008 · doi:10.1080/10652469.2013.824436 |
| [8] | Park, J., Some Hermite-Hadamard type inequalities for MT-convex functions via classical and Riemann-Liouville fractional integrals, Applied Mathematical Sciences, 9, 101, 5011-5026 (2015) · doi:10.12988/ams.2015.56425 |
| [9] | Mohammed, P.; Hamasalh, F., New Conformable fractional integral inequalities of Hermite-Hadamard type for convex functions, Symmetry, 11, 2, 263 (2019) · Zbl 1416.26037 · doi:10.3390/sym11020263 |
| [10] | Noor; Aslam, M., Hadamard integrl inequalities for product of two pre-invex function, Nonlinear Analysis Forum, 14, 167-173 (2009) · Zbl 1296.26086 |
| [11] | Hiriart-Urruty, J. B.; Lemarechal, C., Convex Analysis and Minimization Algorithim, 1 and 2 (1993), Berlin, Germany: Springer, Berlin, Germany · Zbl 0795.49001 |
| [12] | Rockafellar, R. T., Convex Analysis (1970), Princeton, NJ, USA: Princeton University Press, Princeton, NJ, USA · Zbl 0229.90020 |
| [13] | Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204 (2006), New York-London: Elsevier, New York-London · Zbl 1092.45003 |
| [14] | Lazarevic, M., Advanced topics on applications of fractional calculus on control problems, system stability and modelings (2014), WSEAS Press |
| [15] | Denton, Z.; Vatsala, A. S., Fractional integral inequalities and applications, Computers and Mathematics with Applications, 59, 3, 1087-1094 (2010) · Zbl 1189.26044 · doi:10.1016/j.camwa.2009.05.012 |
| [16] | Tariboon, J.; Ntouyas, S. K.; Sudsutad, W., Some New Riemann-Liouville Fractional Integral Inequalities, International Journal of Mathematics and Mathematical Sciences, 2014 (2014) · Zbl 1286.26020 · doi:10.1155/2014/869434 |
| [17] | Odibat, Z., Approximations of fractional integrals and Caputo fractional derivatives, Applied Mathematics and Computation, 178, 2, 527-533 (2006) · Zbl 1101.65028 · doi:10.1016/j.amc.2005.11.072 |
| [18] | Almeida, R., A Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation, 44, 460-481 (2017) · Zbl 1465.26005 · doi:10.1016/j.cnsns.2016.09.006 |
| [19] | Taf, S.; Brahim, K., Some new results using Hadamard fractional integral, The International Journal of Nonlinear Analysis and Applications, 7, 1, 103-109 (2016) · Zbl 1359.26021 |
| [20] | Nchama, G. A. M.; Mecıas, A. L.; Richard, M. R., The Caputo-Fabrizio Fractional Integral to Generate Some New Inequalities, Information Sciences Letters, 8, 2, 73-80 (2019) · doi:10.18576/isl/080205 |
| [21] | MBoro Nchama, G. A., New fractional integral inequalities via caputo-fabrizio operator and an open problem concerning an integral inequality, New Trends in Mathematical Sciences, 2, 8, 9-21 (2020) · doi:10.20852/ntmsci.2020.401 |
| [22] | Iscan, I., Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals, Studia Universitatis Babes-Bolyai Mathematica, 60, 3, 355-366 (2016) · Zbl 1374.26041 |
| [23] | Kunt, M.; Iscan, I., On new Hermite-Hadamard-Fejér type inequalities for \(p\)-convex functions via fractional integrals, Communication in Mathematical Modeling and Applications, 2, 1, 1-15 (2016) |
| [24] | Kunt, M.; Iscan, I., Hermite-Hadamard-Fejér type inequalities for \(p\)-convex functions via fractional integrals, Iranian Journal of Science and Technology, Transactions A: Science, 42, 4, 2079-2089 (2018) · doi:10.1007/s40995-017-0352-4 |
| [25] | Butt, S. I.; Pecaric, J., Generalized Hermite-Hadamard’s inequality, Proceedengs of A.Razmadze Mathematical Institute, 163, 9-27 (2013) · Zbl 1298.26068 |
| [26] | Butt, S. I.; Yousaf, S.; Akdemir, A. O.; Dokuyucu, M. A., New Hadamard-type integral inequalities via a general form of fractional integral operators, Chaos, Solitons & Fractals, 148, 111025 (2021) · Zbl 1485.26023 · doi:10.1016/j.chaos.2021.111025 |
| [27] | Butt, S. I.; Kashuri, A.; Tariq, M.; Nasir, J.; Aslam, A.; Gao, W., Hermite-Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications, Advances in Difference Equations, 2020, 1 (2020) · Zbl 1486.26037 · doi:10.1186/s13662-020-02967-5 |
| [28] | Gao, X., A note on the Hermite-Hadamard inequality, Journal of Mathematical Inequalities, 4, 4, 587-591 (2010) · Zbl 1208.26033 · doi:10.7153/jmi-04-52 |
| [29] | Azcar, A.; Nikodem, K.; Roa, G., Fejr-type inequalities for strongly convex functions, Annales Mathematicae Silesianae, 2012, 26, 43-53 (2013) · Zbl 1292.26046 |
| [30] | Macdonald, I. G., Symmetric Functions and Orthogonal Polynomials (1997), Providence, New York, NY, USA: American Mathematical Society, Providence, New York, NY, USA · Zbl 0887.05053 |
| [31] | Fejr, L., Uberdie Fourierreihen, II, Math. Naturwise Anz Ungar. Akad. Wiss, 24, 369-390 (1906) |
| [32] | Mohammed, P. O.; Aydi, H.; Kashuri, A.; Hamed, Y. S.; Abualnaja, K. M., Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry Function Kernels, Symmetry, 13, 4, 550 (2021) · doi:10.3390/sym13040550 |
| [33] | Budak, H.; Usta, F.; Sarikaya, M. Z.; Ozdemir, M. E., On generalization of midpoint type inequalities with generalized fractional integral operators, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113, 769-790 (2018) · Zbl 1423.26035 · doi:10.1007/s13398-018-0514-z |
| [34] | Almutairi, O.; Kılıçman, A., New fractional inequalities of midpoint type via s-convexity and their application, Journal of Inequalities and Applications, 2019, article 267, 267 (2019) · Zbl 1499.26091 · doi:10.1186/s13660-019-2215-3 |
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