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Year 2021, Volume: 50 Issue: 2, 377 - 386, 11.04.2021
https://doi.org/10.15672/hujms.657839

Abstract

References

  • [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.

The sharper form of a Brunn-Minkowski type inequality for boxes

Year 2021, Volume: 50 Issue: 2, 377 - 386, 11.04.2021
https://doi.org/10.15672/hujms.657839

Abstract

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.

References

  • [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.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Gültekin Tınaztepe 0000-0001-7594-1620

Serap Kemali 0000-0001-5804-4127

Sevda Sezer 0000-0001-6448-193X

Zeynep Eken 0000-0002-8939-4653

Publication Date April 11, 2021
Published in Issue Year 2021 Volume: 50 Issue: 2

Cite

APA Tınaztepe, G., Kemali, S., Sezer, S., Eken, Z. (2021). The sharper form of a Brunn-Minkowski type inequality for boxes. Hacettepe Journal of Mathematics and Statistics, 50(2), 377-386. https://doi.org/10.15672/hujms.657839
AMA Tınaztepe G, Kemali S, Sezer S, Eken Z. The sharper form of a Brunn-Minkowski type inequality for boxes. Hacettepe Journal of Mathematics and Statistics. April 2021;50(2):377-386. doi:10.15672/hujms.657839
Chicago Tınaztepe, Gültekin, Serap Kemali, Sevda Sezer, and Zeynep Eken. “The Sharper Form of a Brunn-Minkowski Type Inequality for Boxes”. Hacettepe Journal of Mathematics and Statistics 50, no. 2 (April 2021): 377-86. https://doi.org/10.15672/hujms.657839.
EndNote Tınaztepe G, Kemali S, Sezer S, Eken Z (April 1, 2021) The sharper form of a Brunn-Minkowski type inequality for boxes. Hacettepe Journal of Mathematics and Statistics 50 2 377–386.
IEEE G. Tınaztepe, S. Kemali, S. Sezer, and Z. Eken, “The sharper form of a Brunn-Minkowski type inequality for boxes”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, pp. 377–386, 2021, doi: 10.15672/hujms.657839.
ISNAD Tınaztepe, Gültekin et al. “The Sharper Form of a Brunn-Minkowski Type Inequality for Boxes”. Hacettepe Journal of Mathematics and Statistics 50/2 (April 2021), 377-386. https://doi.org/10.15672/hujms.657839.
JAMA Tınaztepe G, Kemali S, Sezer S, Eken Z. The sharper form of a Brunn-Minkowski type inequality for boxes. Hacettepe Journal of Mathematics and Statistics. 2021;50:377–386.
MLA Tınaztepe, Gültekin et al. “The Sharper Form of a Brunn-Minkowski Type Inequality for Boxes”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, 2021, pp. 377-86, doi:10.15672/hujms.657839.
Vancouver Tınaztepe G, Kemali S, Sezer S, Eken Z. The sharper form of a Brunn-Minkowski type inequality for boxes. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):377-86.