Generalised HermiteHadamard type inequalities for \((s,r)\)convex functions in mixed kind with applications
Volume 30, Issue 4, pp 372380
http://dx.doi.org/10.22436/jmcs.030.04.06
Publication Date: February 18, 2023
Submission Date: December 15, 2022
Revision Date: January 16, 2023
Accteptance Date: January 30, 2023
Authors
F. Mehmood
 Department of Mathematics, Samarkand State University, Samarkand 140104, Uzbekistan.
 Department of Mathematics, Dawood University of Engineering and Technology, Karachi74800, Pakistan.
F. Nawaz
 Department of Mathematics, Dawood University of Engineering and Technology, Karachi74800, Pakistan.
A. Soleev
 Department of Mathematics, Samarkand State University, Samarkand 140104, Uzbekistan.
Abstract
In this article, some generalized inequalities of the HermiteHadamard type for functions whose modulus of the derivatives are \((s,r)\)convex in mixed kind and applications for probability theory and numerical integration are given. Various established results of different articles would be recaptured as special cases. We also provide special cases of the class of \((s,r)\)convex function on several choices of \(s,r\).
Share and Cite
ISRP Style
F. Mehmood, F. Nawaz, A. Soleev, Generalised HermiteHadamard type inequalities for \((s,r)\)convex functions in mixed kind with applications, Journal of Mathematics and Computer Science, 30 (2023), no. 4, 372380
AMA Style
Mehmood F., Nawaz F., Soleev A., Generalised HermiteHadamard type inequalities for \((s,r)\)convex functions in mixed kind with applications. J Math Comput SCIJM. (2023); 30(4):372380
Chicago/Turabian Style
Mehmood, F., Nawaz, F., Soleev, A.. "Generalised HermiteHadamard type inequalities for \((s,r)\)convex functions in mixed kind with applications." Journal of Mathematics and Computer Science, 30, no. 4 (2023): 372380
Keywords
 Convex function
 HermiteHadamard inequality
 Hölder inequality
 powermean inequality
 numerical integration
 probability density function
MSC
 26A33
 26A51
 26D15
 26D99
 47A30
 33B10
References

[1]
M. Alomari, M. Darus, S. S. Dragomir, Inequalities of HermiteHadamard’s type for functions whose derivatives absolute values are quasiconvex, RGMIA Res. Rep. Coll., 12 (2009), 11 pages

[2]
E. F. Beckenbach, Convex functions, Bull. Amer. Math. Soc., 54 (1948), 439–460

[3]
S. S. Dragomir, On some new inequalities of HermiteHadamard type for mconvex functions, Tamkang J. Math., 33 (2002), 55–65

[4]
S. S. Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91–95

[5]
S. S. Dragomir, J. Peˇcari´c, L. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335–341

[6]
A. Ekinci, Klasik E¸sitsizlikler Yoluyla Konveks Fonksiyonlar i¸cin Integral E¸sitsizlikler, Ph.D. Thesis, Atat ¨ urk University, (2014),

[7]
E. K. Godunova, V. I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions, Numer. Math. Math. Phys. (Russian), 166 (1985), 138–142

[8]
A. Hassan, A. R. Khan, Generalization of Ostrowski inequality via fractional integrals, Submitted, (),

[9]
H. Kavurmaci, M. Avci, M. E. O¨ zdemir, New inequalities of hermitehadamard type for convex functions with applications, J. Inequal. Appl., 2011 (2011), 11 pages

[10]
A. R. Khan, F. Mehmood, F. Nawaz, A. Nazir, Some Remarks on Results Related to rConvex Function, J. Math. Fund. Sci., 53 (2021), 67–85

[11]
U. S. Kirmaci, Improvement and further generalization of inequalities for differentiable mappings and applications, Comput. Math. Appl., 55 (2008), 485–493

[12]
U. S. Kirmaci, M. Klaricˇic´ Bakula, M. E. O¨ zdemir, J. Pecˇaric´, Hadamardtype inequalities for sconvex functions, Appl. Math. Comput., 193 (2007), 26–35

[13]
W. J. Liu, W. S. Wen, J. K. Park, HermiteHadamard type inequalities for MTconvex functions via classical integrals and fractional integrals, J. Nonlinear Sci. Appl., 9 (2016), 766–777

[14]
D. S. Mitrinovi´c, I. B. Lackovi´, Hermite and convexity, Aequationes Math., 28 (1985), 229–232

[15]
M. A. Noor, M. U. Awan, Some integral inequalities for two kinds of convexities via fractional integrals, Transylv. J. Math. Mech., 5 (2013), 129–136

[16]
A. OwusuHemeng, P. Kwasi Sarpong, J. AckoraPrah, The Role of Concave and Convex Functions in the Study of Linear & NonLinear Programming, Dama International Journal of Researchers, 3 (2018), 15–29

[17]
C. E. M. Pearce, J. Peˇcari´, Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13 (2000), 51–55

[18]
J. E. Peˇcari´c, F. Proschan, Y. L. Tong, Convex functions, partial orderings, and statistical applications, Academic Press, Boston (1992)

[19]
M. Z. Sarikaya, E. Set, M. E. O¨ zdemir, On some new inequalities of Hadamard type involving hconvex functions, Acta Math. Univ. Comenian. (N.S.), 79 (2010), 265–272