Some integral inequalities involving the k-Beta function using (m, h_{1}, h_{2})-convex functions.
Keywords:
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
Abstract
The present work deals with the study of the integral of the type
_5.43_.35_p_.%C2%A0m_._.png)
for $ p,q,k > 0 $, considering some inequalities for $ (m,h_{1},h_{2})- $convex functions. From these results some others integral inequalities for other class of generalized convex functions are obtained.
Visitas al artículo
101
Downloads
Download data is not yet available.
References
[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)
[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)
Published
2021-08-19
How to Cite
Hernández Hernández, J. E. (2021). Some integral inequalities involving the k-Beta function using (m, h_{1}, h_{2})-convex functions. Revista MATUA ISSN: 2389-7422, 8(1), 101-113. Retrieved from https://investigaciones.uniatlantico.edu.co/revistas/index.php/MATUA/article/view/3010
Section
Artículos
