Araştırma Makalesi
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Yıl 2021, Cilt 50, Sayı 2, 377 - 386, 11.04.2021
https://doi.org/10.15672/hujms.657839

Öz

Kaynakça

  • [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

Yıl 2021, Cilt 50, Sayı 2, 377 - 386, 11.04.2021
https://doi.org/10.15672/hujms.657839

Öz

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.

Kaynakça

  • [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.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Gültekin TINAZTEPE (Sorumlu Yazar)
AKDENIZ UNIVERSITY
0000-0001-7594-1620
Türkiye


Serap KEMALİ
AKDENIZ UNIVERSITY
0000-0001-5804-4127
Türkiye


Sevda SEZER
AKDENIZ UNIVERSITY
0000-0001-6448-193X
Türkiye


Zeynep EKEN
AKDENİZ ÜNİVERSİTESİ
0000-0002-8939-4653
Türkiye

Yayımlanma Tarihi 11 Nisan 2021
Yayınlandığı Sayı Yıl 2021, Cilt 50, Sayı 2

Kaynak Göster

Bibtex @araştırma makalesi { hujms657839, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2021}, volume = {50}, pages = {377 - 386}, doi = {10.15672/hujms.657839}, title = {The sharper form of a Brunn-Minkowski type inequality for boxes}, key = {cite}, author = {Tınaztepe, Gültekin and Kemali, Serap and Sezer, Sevda and Eken, Zeynep} }
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 . DOI: 10.15672/hujms.657839
MLA 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 50 (2021 ): 377-386 <https://dergipark.org.tr/tr/pub/hujms/issue/61276/657839>
Chicago 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 50 (2021 ): 377-386
RIS TY - JOUR T1 - The sharper form of a Brunn-Minkowski type inequality for boxes AU - Gültekin Tınaztepe , Serap Kemali , Sevda Sezer , Zeynep Eken Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.657839 DO - 10.15672/hujms.657839 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 377 EP - 386 VL - 50 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.657839 UR - https://doi.org/10.15672/hujms.657839 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics The sharper form of a Brunn-Minkowski type inequality for boxes %A Gültekin Tınaztepe , Serap Kemali , Sevda Sezer , Zeynep Eken %T The sharper form of a Brunn-Minkowski type inequality for boxes %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 2 %R doi: 10.15672/hujms.657839 %U 10.15672/hujms.657839
ISNAD Tınaztepe, Gültekin , Kemali, Serap , Sezer, Sevda , Eken, Zeynep . "The sharper form of a Brunn-Minkowski type inequality for boxes". Hacettepe Journal of Mathematics and Statistics 50 / 2 (Nisan 2021): 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. 2021; 50(2): 377-386.
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): 377-386.
IEEE G. Tınaztepe , S. Kemali , S. Sezer ve Z. Eken , "The sharper form of a Brunn-Minkowski type inequality for boxes", Hacettepe Journal of Mathematics and Statistics, c. 50, sayı. 2, ss. 377-386, Nis. 2021, doi:10.15672/hujms.657839