Hermite–Hadamard type inequalities via weighted integral operators

• Kórus, Péter ^[1] ; Nápoles Valdés, Juan Eduardo ^[2] ; Quevedo Cubillos, María Nubia ^[3]
  1. [1] University of Szeged

     University of Szeged

     Hungría

     
  2. [2] Universidad Nacional del Nordeste

     Universidad Nacional del Nordeste

     Argentina

     
  3. [3] Universidad Militar Nueva Granada

     Universidad Militar Nueva Granada

     Colombia

     

  Mostrar afiliaciones +
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 6, 2023, págs. 1499-1519
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5497
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we consider general convex functions of various type. We establish some new integral inequalities of Hermite--Hadamard type for $(h,s,m)$-convex and $(h,m)$-convex functions, using generalized integrals. We also investigate differentiable functions with general convex derivative. The proven results generalize many results previously known from the literature.

• Referencias bibliográficas
  • P. Agarwal, M. Jleli, and M. Tomar, “Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals”, J. Inequal. Appl.,...
  • A. Akkurt, M. E. Yildirim, and H. Yildirim, “On some integral inequalities for (k, h)-Riemann-Liouville fractional integral”, New Trends in...
  • M. A. Ali, J. E. Nápoles V., A. Kashuri, and Z. Zhang, “Fractional non conformable Hermite-Hadamard inequalities for generalized φ-convex...
  • M. Alomari and M. Darus, “Some Ostrowski Type Inequalities for Quasi-Convex Functions with Applications to Special Means”, RGMIA Res. Rep....
  • M. U. Awan, M. A. Noor, F. Safdar, A. Islam, M. V. Mihai, and K. I. Noor, “Hermite-Hadamard type inequalities with applications”, Miskolc...
  • S. Bermudo, P. Kórus, and J. E. Nápoles Valdés, “On q-Hermite-Hadamard inequalities for general convex functions”, Acta Math. Hungar., vol....
  • M. Bessenyei and Z. Páles, “On generalized higher-order convexity and Hermite-Hadamard-type inequalities”, Acta Sci. Math. (Szeged), vol....
  • W. W. Breckner, “Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen”, Publ. Inst....
  • A. M. Bruckner and E. Ostrow, “Some function classes related to the class of convex functions”, Pacific J. Math., vol. 12, no. 4, pp. 1203-1215,...
  • R. Díaz and E. Pariguan, “On hypergeometric functions and Pochhammer k-symbol”, Divulg. Mat., 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 trapezoidal...
  • S. S. Dragomir and S. Fitzpatrick, “The Hadamard’s inequality for s-convex functions in the second sense”, Demonstratio Math., vol. 32, no....
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University,...
  • S. S. Dragomir, J. Pecaric, and L. E. Persson, “Some inequalities of Hadamard type”, Soochow J. Math., vol. 21, pp. 335-341, 1995.
  • G. Farid, A. U. Rehman, and Q. U. Ain, “k-fractional integral inequalities of Hadamard type for (h−m)−convex functions”, Computational Methods...
  • G. Farid, A. U. Rehman, and M. Zahra, “On Hadamard inequalities for k-fractional integrals”, Nonlinear Funct. Anal. Appl., vol. 21, no. 3,...
  • P. M. Guzmán, J. E. Nápoles Valdés, and Y. S. Gasimov, “Integral inequalities within the framework of generalized fractional integrals”, Fractional...
  • J. Hadamard, “Étude sur les propriétés des fonctions entiéres et en particulier d’une fonction considérée par Riemann”, J. Math. Pures Appl....
  • C. Hermite, “Sur deux limites d’une intégrale définie”, Mathesis, vol. 3, no. 82, 1883.
  • J. E. Hernández Hernández, “On Some New Integral Inequalities Related With The Hermite-Hadamard Inequality via h-Convex Functions”, MAYFEB...
  • R. Hussain, A. Ali, G. Gulshan, A. Latif, and K. Rauf, “Hermite-Hadamard Type Inequalities for k-Riemann Liouville Fractional Integrals Via...
  • D. A. Ion, “Some estimates on the Hermite-Hadamard inequality through quasi-convex functions”, Annals of University of Craiova, Math. Comp....
  • M. A. Khan and Y. Khurshid, “Hermite-Hadamard’s inequalities for η-convex functions via conformable fractional integrals and related inequalities”,...
  • U. S. Kirmaci, “Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula”, Appl....
  • M. Klaričić, E. Neuman, J. Pečiarić, and V. Simić, “Hermite-Hadamard’s inequalities for multivariate g-convex functions”, Math. Inequal. Appl.,...
  • M. Klaričić Bakula, M. E. Ozdemir, and J. Pečiarić, “Hadamard Type Inequalities for m-Convex and (α, m)-Convex Functions”, J. Inequal. Pure...
  • P. Kórus and J. E. Nápoles Valdés, “Some Hermite-Hadamard inequalities involving weighted integral operators via (h, s, m)-convex functions”,...
  • M. Matloka, “On some integral inequalities for (h, m)-convex functions”, Mathematical Economics, vol. 9, no. 16, pp. 55-70, 2013.
  • V. G. Mihesan, “A generalization of the convexity”, Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca (Romania), 1993.
  • M. S. Moslehian, “Matrix Hermite-Hadamard type inequalities”, Houston J. Math., vol. 39, no. 1, pp. 177-189, 2013.https://doi.org/10.48550/arXiv.1203.5300
  • S. Mubeen and G. M. Habibullah, “k-Fractional Integrals and Application”, Int. J. Contemp. Math. Sci., vol. 7, no. 2, pp. 89-94, 2012.
  • M. Muddassar, M. I. Bhatti, and W. Irshad, “Generalisation of integral inequalities of Hermite-Hadamard type through convexity”, Bull. Aust....
  • J. E. Nápoles Valdés, F. Rabossi, and A. D. Samaniego, “Convex functions: Ariadne’s thread or Charlotte’s Spiderweb?”, Advanced Mathematical...
  • J. E. Nápoles Valdés, J. M. Rodríguez, and J. M. Sigarreta, “On Hermite-Hadamard type inequalities for non-conformable integral operators”,...
  • M. A. Noor, K. I. Noor, and M. U. Awan, “Generalized fractional Hermite-Hadamard inequalities”, Miskolc Math. Notes, vol. 21, no. 2, pp. 1001-1011,...
  • M. E. Özdemir, S. S. Dragomir, and C. Yildiz, “The Hadamard Inequality For Convex Function Via Fractional Integrals”, Acta Math. Sci., vol....
  • M. E. Özdemir, H. Kavurmaci, and M. Avci, “Ostrowski type inequalities for convex functions”, Tamkang J. Math., vol. 45, no. 4, pp. 335-340,...
  • J. Park, “Some Hermite-Hadamard type inequalities for MT-convex functions via classical and Riemann-Liouville fractional integrals”, Appl....
  • C. E. M. Pearce and J. Pečiarić, “Inequalities for differentiable mappings with application to special means and quadrature formulae”, Appl....
  • F. Qi and B.-N. Guo, “Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function”,...
  • E. D. Rainville, Special Functions. New York: Macmillan Co., 1960.
  • M. Rostamian Delavar, S. S. Dragomir, and M. De La Sen, “Estimation type results related to Fejér inequality with applications”, J. Inequal....
  • M. Z. Sarikaya, “On new Hermite Hadamard Fejér Type integral inequalities”, Stud. Univ. Babeş-Bolyai Math., vol. 57, no. 3, pp. 377-386, 2012.
  • M. Z. Sarikaya, A. Saglam, and H. Yildirim, “New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values...
  • M. Z. Sarikaya, E. Set, H. Yaldiz, and N. Basak, “Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities”,...
  • M. Z. Sarikaya and H. Yildirim, “On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals”, Miskolc Math. Notes, vol....
  • E. Set, J. Choi, and A. Gözpinar, “Hermite-Hadamard Type Inequalities Involving Nonlocal Conformable Fractional Integrals”, Malaysian Journal...
  • E. Set and A. Gözpinar, “A study on Hermite-Hadamard type inequalities for s-convex functions via conformable fractional integrals”, Stud....
  • E. Set, A. Gözpinar, and A. Ekinci, “Hermite-Hadamard type inequalities via conformable fractional integrals”, Acta Math. Univ. Comenianae,...
  • G. Toader, “Some generalizations of the convexity”, Proceedings of the Colloquium on Approximation and Optimization, University ClujNapoca,...
  • B.-Y. Xi, D.-D. Gao, and F. Qi, “Integral inequalities of Hermite-Hadamard type for (α, s)-convex and (α, s, m)-convex functions”, Ital. J....
  • B.-Y. Xi, Y. Wang, and F. Qi, “Some integral inequalities of Hermite-Hadamard type for extended (s, m)-convex functions”, Transylv. J. Math....
  • Z.-H. Yang and J.-F. Tian, “Monotonicity and inequalities for the gamma function”, J. Inequal. Appl., vol. 2017, 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”, J. Math. Inequal., vol. 12, no. 1, pp. 1-22, 2018....
  • C. Yildiz, M. E. Özdemir, and H. K. ̈Önalan, “Fractional Integral Inequalities via s-Convex Functions”, Turkish Journal of Analysis and Number...
  • C. Zhu, M. Feckan, and J. Wang, “Factional integral inequalities for differential convex mappings and applications to special means and a...