SOME WEIGHTED SIMPSON-LIKE TYPE INEQUALITIES FOR DIFFERENTIABLE beta-PREINVEX FUNCTIONS

Hayet Bahloul, Salim Hamida, Badreddine Meftah, Abdelhak Djebabla

DOI Number
https://doi.org/10.22190/FUMI220825032B
First page
487
Last page
507

Abstract


In this paper, we first prove a new identity based on which we have established some weighted Simpson-type inequalities for functions whose first derivatives are beta-preinvex. Some applications of our finding are proposed.


Keywords

Simpson-like type inequalities, beta-preinvex functions, weighted function, P-functions

Full Text:

PDF

References


bibitem{1} {sc M. A. Ali, M. Abbas, H. Budak, P. Agarwal, G. Murtaza and Y.-M.

Chu}: textit{New quantum boundaries for quantum Simpson's and quantum Newton's type

inequalities for preinvex functions}. Adv. Difference Equ. 2021, Paper No.

{bf 64}, 21 pp.

bibitem{2} {sc P. Agarwal, S. S. Dragomir, M. Jleli and B. Bessem}: textit{Advances in

Mathematical Inequalities and Applications}. Trends in Mathematics. Birkh"{a}%

user/Springer, Singapore, 2018.

bibitem{3} {sc W. W. Breckner}: textit{Stetigkeitsaussagen f"{u}r eine Klasse

verallgemeinerter konvexer Funktionen in topologischen linearen R"{a}umen}.

(German) Publ. Inst. Math. (Beograd) (N.S.) {bf 23} (37) (1978), 13--20.

bibitem{4} {sc H. Budak, F. Hezenci and H. Kara}: textit{On parameterized inequalities

of Ostrowski and Simpson type for convex functions via generalized

fractional integrals}. Math. Methods Appl. Sci. {bf 44} (2021), no. 17,

--12536.

bibitem{5} {sc H. Budak, F. Hezenci and H. Kara}: textit{On generalized Ostrowski,

Simpson and trapezoidal type inequalities for co-ordinated convex functions

via generalized fractional integrals}. Adv. Difference Equ. 2021, Paper No.

, 32 pp.

bibitem{6} {sc S. I. Butt, I. Javed, P. Agarwal and J. J. Nieto}: textit{Newton-Simpson-type inequalities via majorization}. J. Inequal. Appl. 2023,

Paper No. 16.

bibitem{7} {sc T. Chiheb, N. Boumaza and B. Meftah}: textit{Some new Simpson-like type

inequalities via preqausiinvexity}. Transylv. J. Math. Mech. {bf 12} (2020), no.1,

-10.

bibitem{8} {sc S. S. Dragomir, J. E. Pev{c}ari'{c} and L. E. Persson}: textit{Some

inequalities of Hadamard type}. Soochow J. Math. {bf 21} (1995), no. 3, 335--341.

bibitem{9} {sc S. S. Dragomir}: textit{Inequalities of Hermite-Hadamard type for $h$%

-convex functions on linear spaces}. Proyecciones {bf 34} (2015), no. 4, 323--341.

bibitem{10} {sc E. K. Godunova and V. I. Levin}: textit{Inequalities for functions of a

broad class that contains convex, monotone and some other forms of

functions}. (Russian) Numerical mathematics and mathematical physics

(Russian), 138--142, 166, Moskov. Gos. Ped. Inst., Moscow, 1985.

bibitem{11} {sc S. Hamida and B. Meftah}: textit{Some Simpson type inequalities for

differentiable $h$-preinvex functions}. Indian J. Math. {bf} 62 (2020), no. 3,

--319.

bibitem{12} {sc M. A. Hanson}: textit{On sufficiency of the Kuhn-Tucker conditions}. J.

Math. Anal. Appl. {bf 80} (1981), no. 2, 545--550.

bibitem{13} {sc F. Hezenci, H. Budak and H. Kara}: textit{New version of fractional

Simpson type inequalities for twice differentiable functions}. Adv.

Difference Equ. 2021, Paper No. 460, 10 pp.

bibitem{14} {sc A. Kashuri, B. Meftah and P.O. Mohammed}: textit{Some weighted Simpson

type inequalities for differentiable $s$-convex functions and their

applications}. J. Frac. Calc. & Nonlinear Sys. {bf 1} (2021) no. 1, 75-94.

bibitem{15} {sc A. A. Kilbas, H. M. Srivastava and J. J. Trujillo}: textit{Theory and

applications of fractional differential equations}. North-Holland Mathematics

Studies, 204. Elsevier Science B.V., Amsterdam, 2006.

bibitem{16} {sc U. S. Kirmaci}: textit{Refinements of Hermite-Hadamard type inequalities

for $s$-convex functions with Applications to Special Means}. Universal

Journal of Mathematics and Applications, {bf 4} (2021) no.3, 114-124.

bibitem{17} {sc J.-Y. Li}: textit{On Hadamard-type inequalities for $s$-preinvex

functions}. Journal of Chongqing Normal University (Natural Science)

{bf 27} (2010), no. 4, p. 003.

bibitem{18} {sc C.-Y. Luo, C.-S. Du, M. Kunt and Y. Zhang}: textit{Certain new bounds

considering the weighted Simpson-like type inequality and applications}. J.

Inequal. Appl. 2018, Paper No. 332, 20 pp.

bibitem{19} {sc B. Meftah and K. Mekalfa}: textit{Some weighted trapezoidal inequalities

for differentiable $log $-convex functions}. J. Interdiscip. Math. {bf 23}

(2020), 1-13.

bibitem{20} {sc B. Meftah and K. Mekalfa}: textit{Some weighted trapezoidal type

inequalities via $h$-preinvexity.} Rad Hrvat. Akad. Znan. Umjet. Mat. Znan.

{bf 24} (2020), 81-97.

bibitem{21} {sc B. Meftah and K. Mekhalfa}: textit{Some weighted trapezoidal inequalities

for prequasiinvex functions}. Commun. Optim. Theory {bf 2020} (2020), ArticleID20.

bibitem{22} {sc B. Meftah, M. Benssaad, W. Kaidouchi and S. Ghomrani}: textit{Conformable

fractional Hermite-Hadamard type inequalities for product of two harmonic $s$%

-convex functions}. Proc. Amer. Math. Soc. {bf 149} (2021), no. 4, 1495--1506.

bibitem{23} {sc K. Mehrez and P. Agarwal}: textit{New Hermite-Hadamard type integral

inequalities for convex functions and their applications}. J. Comput. Appl.

Math. {bf 350} (2019), 274--285.

bibitem{24} {sc M. A. Noor, K. I. Noor, M. U. Awan and S. Khan}: textit{Hermite-Hadamard

inequalities for $s$-Godunova-Levin preinvex functions}, J. Adv. Math. Stud.

{bf 7} (2014), no. 2, 12-19.

bibitem{25} {sc M. A. Noor, K. I. Noor, M. U. Awan and J. Li}: textit{On Hermite-Hadamard

inequalities for $h$-preinvex functions}, Filomat, {bf} 28 (2014), no. 7,

-1474.

bibitem{26} {sc M. A. Noor, M. U. Awan and K. I. Noor}: textit{Some new bounds of the

quadrature formula of Gauss-Jacobi type via $(p,q)$-preinvex functions}.

Appl. Math. Inform. Sci. Lett, {bf 5} (2017), no 2, 51-56.

bibitem{27} {sc M. A.Noor,K. I. Noor and S. Iftikhar}: textit{Harmonic $beta$-preinvex

functions and inequalities}. Int. J. Anal. Appl., {bf 13} (2017), no 1, 41-53.

bibitem{28} {sc J. E. Pev{c}ari'{c}, F. Proschan and Y. L. Tong}: textit{Convex

functions, partial orderings, and statistical applications}. Mathematics in

Science and Engineering, 187. Academic Press, Inc., Boston, MA, 1992.

bibitem{29} {sc M. Z. Sarikaya}: textit{On new Hermite Hadamard Fej'{e}r type integral

inequalities}. Stud. Univ. Babec{s}-Bolyai Math. {bf} 57 (2012), no. 3, 377--386.

bibitem{30} {sc E. Set, .{I}. .{I}c{s}can, M. Z. Sarikaya and M. E. "{O}%

zdemir}: textit{On new inequalities of Hermite-Hadamard-Fej'{e}r type for convex

functions via fractional integrals}. Appl. Math. Comput. {bf} 259 (2015), 875--881.

bibitem{31} {sc Y. Shuang, Y. Wang and F. Qi}: textit{Integral inequalities of Simpson's

type for $(alpha ,m)$-convex functions}. J. Nonlinear Sci. Appl. {bf} 9 (2016),

no. 12, 6364--6370.

bibitem{32} {sc M. Tunc{c}, E. G"{o}v, and "{U}. c{S}anal}: textit{On $tgs$-convex function and their inequalities}. Facta Univ. Ser. Math. Inform. {bf} 30 (2015), no. 5, 679--691.

bibitem{33} {sc M. Tunc{c}, U. Sanal and E. Gov}: textit{Some Hermite-Hadamard

inequalities for $beta$-convex and its fractional applications.} New Trends

in Mathematical Sciences, {bf 3} (2015), no 4, p. 18.

bibitem{34} {sc T. Weir and B. Mond}: textit{Pre-invex functions in multiple objective

optimization.} J. Math. Anal. Appl. {bf 136} (1988), no. 1, 29-38.

bibitem{35} {sc X. You, F. Hezenci, H. Budak and H. Kara}: textit{New Simpson type inequalities for twice differentiable functions via generalized fractional

integrals.} AIMS Math. {bf 7} (2022), no. 3, 3959--3971.




DOI: https://doi.org/10.22190/FUMI220825032B

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)