Algunas desigualdades integrales que involucran la función $ k- Beta usando funciones (m, h_{1}, h_{2})-Convexas

  • Jorge Eliecer Hernández Hernández Universidad Centroccidental Lisandro Alvarado
Palabras clave: Integral inequalities, $ (m,h_{1},h_{2})- $convex functions, $ k- $Beta function Desigualdades integrales \sep funciones $ (m,h_{1},h_{2})- $convexas, Funci\'{o}n $ k- $Beta

Resumen

El presente trabajo trata acerca del estudio de la integral del tipo 

  Captura_de_Pantalla_2021-08-19_a_la(s)_5.43_.35_p_. m_._.png

    para $ p,q,k > 0 $, considerando algunas desigualdades para funciones $(m,h_{1},h_{2})- $convexas. De estos  resultados se derivan algunas otras desigualdades integrales para otras clases de funciones convexas generalizadas.

Visitas al artículo

47

Descargas

La descarga de datos todavía no está disponible.

Biografía del autor/a

Jorge Eliecer Hernández Hernández, Universidad Centroccidental Lisandro Alvarado

Universidad Centroccidental Lisandro Alvarado, Decanato de Ciencias Económicas y Empresariales, Departamento de Técnicas Cuantitativas, Barquisimeto, Venezuela

Referencias

[1] M. Alomari and M. Darus, On The Hadamard’s Inequality for Log-Convex Functions on the Coordi- nates, J. Ineq. Appl., 2009 (2009), Article ID 283147, 13 pp,
[2] M. Alomari, M. Darus, S.S. Dragomir and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense. Appl.Math. Lett., 23 (2010), 1071-1076
[3] M. Bombardelli and S. Varosˇanec. Properties of h-convex functions related to the Hermite-Hadamard- Fe ́jer inequalities. Computers and Mathematics with Applications. 58(9) (2009), 1869-1877
[4] G. Cristescu, M.A. Noor and M.U. Awan. Bounds of the second degree cumulative frontier gaps of functions with generalized convexity. Carpath. J. Math., 31 (2015), 173aˆ180
[5] G. Cristescu, M. Ga ̆ianu and A. M. Uzair. Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions. Anal. Univ. Vest, Timisoara Ser. Mat. Inf., LIII (1) (2015), 19aˆ35
[6] R. Diaz and E. Pariguan. On hypergeometric functions and Pochhammer k-symbol. Divulgaciones Ma- tema ́ticas, 15 (2) (2007), 179-192
[7] S. S. Dragomir, J. Pecˇaric ́ and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (3) (1995), 335 - 341.
[8] S.S. Dragomir and S. Fitzpatrick, The Hadamard Inequalities for s−convex functions in the second sense , Demostratio Mathematica, 4 (1999), 687-696.
[9] A. Hassibi, J. P. How and S. Boyd, Low-authority controller design via convex optimization, AIAA Journal of Guidance, Control, and Dynamics, 22(6) (1999), 862-872.
[10] J.E. Herna ́ndez H, On a Hardy’s inequality for a fractional integral operator, Annals of the University of Craiova, Mathematics and Computer Science Series, 45(2) (2018), 232-242
[11] J. E. Herna ́ndez Herna ́ndez. Some integral inequalities involving the k−Beta function using h−convex functions. Lecturas Matema ́ticas. 41(1)(2020), 5-17
[12] J.-B. Hiriart-Urruty, Global optimality conditions in maximizing a convex quadratic function under convex quadratic constraints, J. Global Optim. 21 (2001), 445-455.
[13] H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), 100-111
[14] W.Liu,SomeNewIntegralInequalitiesviaP−convexity,arxiv:1202.0127v1[math.FA].1(2012),avai- lable in: http://arxiv.org/abs/1202.0127
[15] M.E.O ̈zdemir,E.SetandM.Alomari,Integralinequalitiesviaseveralkindsofconvexity.Creat.Math. Inform. 20 (1) (2011), 62 - 73
[16] Z. Pavic ́ and M. Avci Ardic, The most important inequalities for m-convex functions. Turk J. Math. 41 (2017), 625-635.
[17] B. T. Polyak, Convexity of quadratic transformations and its use in control and optimization,J. Optim. Theory Appl. 99 (1998), 553-583.
[18] A. Rehman, S. Mubeen, R. Safdar and N. Sadiq. Properties of k−Beta function with several variables, Open Math. 13 (2015) , 308-320
[19]M.Z.Sarikaya,E.SetandM.E.O ̈zdemir,OnsomenewinequalitiesofHadamardtypeinvolving h−convex functions. Acta Math. Univ. Comenian. 79(1) (2010), 265 - 272.
[20] E. Set, A. Akdemir and N. Uygun, On new simpson type inequalities for generalized quasi-convex mappings, Xth International Statistics Days Conference, 2016, Giresun, Turkey
[21] Shi, D-P., Xi B-Y., Qi, F. Hermite–Hadamard Type Inequalities for (m, h1, h2)−Convex Functions Via Riemann-Liouville Fractional Integrals. Turkish Journal of Analysis and Number Theory. 2(1) (2014), 23-28
[22] S. Varosˇanec, On h−convexity, J. Math. Anal. Appl. 326(1) (2007), 303-311.
[23] M.J.VivasandJ.E.Herna ́ndezH,OnsomenewgeneralizedHermite-Hadamard-Fe ́jerinequalitiesfor
product of two operator h−convex functions. Appl. Math. Inf. Sci. 11(4) (2017), 983-992
[24] M.J. Vivas-Cortez and Y.C. Rangel Oliveros, Ostrowski type inequalities for functions whose second derivatives are convex generalized. App. Math. Inf. Sci. 12 (6) (2018), 1117-1126
[25] M.J.Vivas,C.Garc ́ıaandJ.E.Herna ́ndezH,Ostrowski-typeinequalitiesforfunctionswhosederivative modulus is relatively (m, h1 , h2 )−convex. Appl. Math. Inf. Sci. 13(3) (2019), 369-378
[26] B.Xi,F.Qi.PropertiesandInequalitiesforthe(h1,h2)and(h1,h2,m)−GA-Convexfunctions.Journal Cogent Mathematics. 3 (2016)
Publicado
2021-08-19