The sharper form of a Brunn-Minkowski type inequality for boxes
In this study, the Brunn-Minkowski inequality for boxes is studied and a sharper version of this inequality is derived by performing the results based on abstract convexity.
___
- [1] G.R. Adilov and S. Kemali, Hermite-Hadamard-Type Inequalities For Increasing Positively
Homogeneous Functions, J. Inequal. Appl. 2007, Article ID 21430, 10 pages,
2007.
- [2] G.R. Adilov and S. Kemali, Abstract Convexity and Hermite-Hadamard Type Inequalities,
J. Inequal. Appl., 2009, Article ID 943534, 13 pages, 2009.
- [3] G.R. Adilov and G. Tınaztepe, The Sharpening Some Inequalities via Abstract Convexity,
Math. Inequal. Appl. 12, 33–51, 2012.
- [4] Y.D. Burago and V.A. Zalgaller, Geometric Inequalities, Springer, 1988.
- [5] J.P. Crouzeix, J.E. M. Legaz and M. Volle, Generalized Convexity, Generalized Monotonicity:
Recent Results, Kluwer Academic Publishers, 1998.
- [6] S.S. Dragomir, J. Dutta and A.M. Rubinov, Hermite-Hadamard Type Inequalities For
Increasing Convex Along Rays Functions, Analysis (Munich) 2, 171–181, 2001.
- [7] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite–Hadamard Inequalities
and Applications, Victoria University, Footscray, Australia, 2000.
- [8] S. Jain, K. Mehrez, D. Baleanu and P. Agarwal, Certain Hermite–Hadamard Inequalities
for Logarithmically Convex Functions with Applications, Mathematics 7,
163–175, 2019.
- [9] S. Jhanthanam, J. Tariboon, S.K. Ntouyas and K. Nonlaopon, On q-Hermite-
Hadamard Inequalities for Differentiable Convex Functions, Mathematics 7, 632–641,
2019.
- [10] W. Liu, New Integral Inequalities Via $(\alpha,m)$-Convexity and Quasi-Convexity, Hacet.
J. Math. Stat. 42, 289–297, 2013.
- [11] K. Mehrez and P. Agarwal, New Hermite-Hadamard Type Integral Inequalities for
Convex Functions and Their Applications, J. Comput. Appl. Math. 350, 274–285,
2019.
- [12] M.E. Özdemir, H. Kavurmacı and E. Set, Ostrowski’s Type Inequalities for $(\alpha,m)$-
Convex Functions, Kyungpook Math. J. 50, 371–378, 2010.
- [13] Z. Pavic and M.A. Ardıç, The most important inequalities of m-convex functions,
Turk. J. Math. 41, 625–635, 2017.
- [14] F. Qi and B.Y. Xi, Some Hermite-Hadamard type inequalities for geometrically quasiconvex
functions, Proc. Indian Acad. Sci. (Math. Sci.) 124(3), 333–342, 2014.
- [15] A.M. Rubinov, Abstract Convexity and Global optimization, Springer US, Kluwer
Academic Publishers, 2000.
- [16] A.M. Rubinov and Z.Y. Wu, Optimality Conditions in Global Optimization and Their
Applications, Math. Program. 120(1), 101–123, 2009.
- [17] M.Z. Sarikaya, E. Set, M.E. Özdemir, On new inequalities of Simpson’s Type for s
-convex Functions. Comput. Math. Appl. 60, 2191–2199, 2010.
- [18] I. Singer, Abstract Convex Analysis, Wiley-Interscience, 1997.
- [19] G. Tınaztepe, The sharpening Hölder Inequality via abstract convexity, Turk. J.
Math. 40, 438–444, 2016.
- [20] I. Yesilce and G.R. Adilov, Hermite-Hadamard Inequalities for $L(j)$-convex Functions
and $S(j)$-convex Functions, Malaya J. Mat. 3, 346–359, 2015.
- [21] I. Yesilce and G.R. Adilov, Hermite-Hadamard Inequalities for B-convex and $B^{-1}$-
convex functions, Int. J. Nonlinear Analysis Appl. 8, 225–233, 2017.
- [22] I. Yesilce and G.R. Adilov, Fractional Integral Inequalities for B-convex Functions,
Creat. Math. Inform. 26, 345–351, 2017.