Some extensions of the Hermite-Hadamard inequalities for quasi-convex functions via weighted integral
DOI:
https://doi.org/10.22199/issn.0717-6279-5610Keywords:
convex functions, quasi-convex functions, Hadamard type inequality, integral operators weightedAbstract
References
H. Angulo, J. Giménez, A. M. Moros and K. Nikodem, “On strongly h-convex functions”, Annals of functional analysis, vol. 2, no. 2, pp. 85-91, 2011. https://doi.org/10.15352/afa/1399900197
M. A. Khan, Y.-M. Chu, A. Kashuri, R. Liko and G. Ali, “Conformable fractional integrals versions of Hermite-Hadamard inequalities and their generalizations”, Journal of function spaces, vol. 2018, Art ID. 6928130, 2018. https://doi.org/10.1155/2018/6928130
M. A. Ali, J. E. Nápoles Valdés, A. Kashuri and Z. Zhang, ”Fractional non conformable Hermite-Hadamard inequalities for generalized -convex functions”, Fasciculi Mathematici, vol. 64, pp. 5-16, 2020. https://doi.org/10.21008/j.0044-4413.2020.0007
M. Alomari, M. Darus and S.S. Dragomir, ”New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex”, Tamkang Journal of Mathematisc, vol. 41, no 4, pp. 353-359, 2010.
B. Bayraktar and M. E. Özdemir, ”Generalization Of Hadamard -Type Trapezoid Inequalities For Fractional Integral Operators”, Ufa Mathematical Journal, vol. 13. no. 1, pp. 119-130, 2021. https://doi.org/10.13108/2021-13-1-119
B. Bayraktar, S. Butt, S Shaukat and V. J. Nápoles, “New Hadamard Type Inequalities Via (s, m1, m2)−Convex Functions”, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki, vol. 31, no. 4, pp. 597-612, 2021. https://doi.org/10.35634/Vm210405
S. Bermudo, P. Kórus and J. E. Nápoles Valdés, ”On q-HermiteHadamard inequalities for general convex functions”, Acta Mathematica Hungarica, vol. 162, pp. 364-374, 2020. https://doi.org/10.1007/s10474-020-01025-6
M. Bessenyei and Z. Páles, ”On generalized higher-order convexity and Hermite-Hadamard-type inequalities”, Acta Scientiarum Mathematicarum (Szeged), vol. 70, no. 1-2, pp. 13-24, 2004.
W. W. Breckner, ”Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen”, Publications de l'Institut Mathématique, vol. 23, pp. 13-20, 1978.
R. Díaz, and E. Pariguan, ”On hypergeometric functions and Pochhammer k-symbol”, Divulgaciones Matemáticas, vol. 15, no. 2, pp. 179-192, 2007.
S. S. Dragomir and R. P. Agarwal, ”Two Inequalities for Differentiable Mappings and Applications to Special Means of Real Numbers and to Trapezoidal Formula”, Applied Mathematics Letters, vol. 11, no. 5, pp. 91-95, 1998.
S. S. Dragomir and S. Fitzpatrik, ”The Hadamards inequality for s−convex functions in the second sense”, Demonstratio Mathematica, vol. 32, no. 4, pp. 687-696, 1999.
S. S. Dragomir and C. E. M. Pearce, ”Quasi-convex functions and Hadamard’s inequality”, Bulletin of the Australian Mathematical Society, vol. 57, pp. 377-385, 1998.
S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities. RGMIA Monographs. Victoria University, 2000.
S. S. Dragomir, J. Pecaric and L. E. Persson, ”Some inequalities of Hadamard type”, Soochow Journal of Mathematics, vol. 21, pp. 335-241, 1995.
P. M. Guzmán, Nápoles, J. E. Valdés and Y. Gasimov, “Integral inequalities within the framework of generalized fractional integrals”, Fractional Differential Calculus, vol. 11, no. 1, pp. 69-84, 2021. https://doi.org/10.7153/fdc-2021-11-05
J. E. Hernández Hernández, ”On Some New Integral Inequalities Related With The Hermite-Hadamard Inequality via h−Convex Functions”, MAYFEB Journal of Mathematics, vol. 4, pp. 1-12, 2017.
D. A. Ion, ”Some estimates on the Hermite-Hadamard inequality through quasi-convex functions”, Annals of University of Craiova, Math. Comp. Sci. Ser., vol. 34, pp. 82-87, 2007.
A. Kashuri, M. Raees and M. Anwar, “Some integral inequalities for approximately h−convex functions and their applications”, Proyecciones (Antofagasta), vol. 40, no. 2, pp. 481-504, 2021. https://doi.org/10.22199/issn.0717-6279-2021-02-0028
M. Klaričić, E. Neuman, J. Pečarić, and S. Šimić, ”Hermite-Hadamard’s inequalities for multivariate g-convex functions”, Mathematical Inequalities & Applications, vol. 8, no. 2, pp. 305-316, 2005.
P. Kórus, L. M. Lugo and J. E. Nápoles Valdés, ”Integral inequalities in a generalized context”, Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 3, pp. 312-320, 2020. https://doi.org/10.1556/012.2020.57.3.1464
M. Matloka, ”Hermite-Hadamard Type Inequalities for Fractional Integrals”, RGMIA Res. Rep. Coll., vol. 20, Art. 69. 11, 2017.
M. S. Moslehian, “Matrix Hermite-Hadamard type inequalities”, Houston Journal of Mathematics, vol. 39, no. 1, pp. 177-189, 2013.
J. E., N´apoles Vald´es, B. Bayraktar and S. I. Butt, ”New integral inequalities of Hermite-Hadamard type in a generalized context”, Punjab University Journal of Mathematics, vol. 53, no. 11, pp. 765-777, 2021. https://doi.org/10.52280/pujm.2021.531101
J. E. Nápoles Valdés, F. Rabossi and H. Ahmad, ”Inequalities of the Hermite-Hadamard Type, for functions (h, m)−convex modified of the second type”, Communications in combinatorics, cryptography & computer science, vol. 1, pp. 33-43, 2021.
J. E. N´ apoles Vald´es, F. Rabossi and A. D. Samaniego, ”Convex Functions: Ariadne’s Thread or Charlotte’s Spiderweb?”, Advanced Mathematical Models & Applications, vol. 5, no.2, pp. 176-191, 2020.
J. E. Nápoles Valdés, J. M. Rodríguez and J. M. Sigarreta, ”On Hermite -Hadamard type inequalities for non-conformable integral operators”, Symmetry, vol. 11, pp. 1108, 2019. https://doi.org/10.3390/sym11091108
M. E. Özdemir, ”On Iyengar-type inequalities via quasi-convexity and quasi-concavity”, Miskolc Mathematical Notes, vol. 15, no 1, pp. 171-181, 2014. https://doi.org/10.18514/MMN.2014.644.
M. E. Özdemir, A. Ekinci and A. Akdemir, ”Generalizations of integral inequalities for functions whose second derivatives are convex and m−convex”, Miskolc Mathematical Notes, vol. 13, no. 2, pp. 441-457, 2012. https://doi.org/10.18514/MMN.2012.436.
M. E. Özdemir, M. Gurbuz and E. Yildiz, ”Inequalities for mappings whose second derivatives are quasi-convex or h− convex functions”, Miskolc Mathematical Notes, vol. 15, no. 2, pp. 635-649, 2014. https://doi.org/10.18514/MMN.2014.643.
M. E. Özdemir and C. Yildiz, ”The Hadamard’s inequality for quasi-convex functions via fractional integrals”, Annals of the University of Craiova. Mathematics and Computer Science Series, vol. 40, no. 2, pp. 167-173, 2013.
J. E. Pecaric, F. Proschan and Y. Tong, Convex functions, partial orderings, and statistical applications. Mathematics in Science and Engineering, vol. 187. Boston, MA: Academic Press, 1992.
F. Qi and B.N. Guo, ”Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function”, RACSAM, vol. 111, no. 2, pp. 425-434, 2017. https://doi.org/10.1007/s13398-016-0302-6
E. D. Rainville, Special Functions. New York: Macmillan Co., 1960.
M. Z. Sarikaya, A. Saglam and H. Yildirin, ”On Some Hadamard Inequalities for h−convex Functions”, Journal of Mathematical Inequalities, vol. 2, no. 3, pp. 335-341, 2008.
M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, ”Hermite-Hadamards inequalities for fractional integrals and related fractional inequalities”, Mathematical and Computer Modelling, vol. 57, pp. 2403-2407, 2013. https://doi.org/10.1016/j.mcm.2011.12.048.
S. Varosneac, ”On h−convexity”, Journal of Mathematical Analysis and Applications, vol. 326, pp. 303-311, 2007.
M. Vivas-Cortez, P. Kórus, J. E. Nápoles Valdés, ”Some generalized Hermite-Hadamard-Fejer inequality for convex functions”, Advances in Difference Equations, vol. 2021, pp. 199, 2021. https://doi.org/10.1186/s13662-021-03351-7
J. R. Wang, X. Li and Y. Zhou, ”Hermite-Hadamard Inequalities Involving Riemann-Liouville Fractional Integrals via s-convex Functions and Applications to Special Means”, Filomat, vol. 30, no. 5, pp. 1143-1150, 2016. https://doi.org/10.2298/FIL1605143W
Z. H. Yang and J. E. Tian, Monotonicity and inequalities for the gamma function”, Journal of Inequalities and Applications, vol. 2017, no. 317, 2017. https://doi.org/10.1186/s13660-017-1591-9
Z. H. Yang, and J. F. Tian, “Monotonicity and sharp inequalities related to gamma function”, Journal of Mathematical Inequalities, vol. 12, no. 1, pp. 1-22 2018. https://doi.org/10.7153/jmi-2018-12-01
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