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Journal articles on the topic 'Geometric inequality'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

R., Elakkiya, and Panneer Selvam A. "A STUDY ON GEOMETRIC INEQUALITIES." International Journal of Current Research and Modern Education, Special Issue (August 15, 2017): 88–89. https://doi.org/10.5281/zenodo.843539.

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2

Kotlyar, B. D. "On a geometric inequality." Journal of Soviet Mathematics 51, no. 5 (1990): 2534–36. http://dx.doi.org/10.1007/bf01104168.

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3

Chu, Xiao-Guang, and Jian Liu. "Generalization of a Geometric Inequality." Missouri Journal of Mathematical Sciences 21, no. 3 (2009): 155–62. http://dx.doi.org/10.35834/mjms/1316024881.

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4

Bracken, Paul. "An arithmetic-geometric mean inequality." Expositiones Mathematicae 19, no. 3 (2001): 273–79. http://dx.doi.org/10.1016/s0723-0869(01)80006-2.

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5

Liu, Jian. "A geometric inequality with applications." Journal of Mathematical Inequalities, no. 3 (2016): 641–48. http://dx.doi.org/10.7153/jmi-10-51.

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6

Eddy, Roland H. "Behold! The Arithmetic-Geometric Mean Inequality." College Mathematics Journal 16, no. 3 (1985): 208. http://dx.doi.org/10.2307/2686572.

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7

Sababheh, Mohammad, Shigeru Furuichi, Zahra Heydarbeygi, and Hamid Reza Moradi. "On the arithmetic-geometric mean inequality." Journal of Mathematical Inequalities, no. 3 (2021): 1255–66. http://dx.doi.org/10.7153/jmi-2021-15-84.

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8

Hayashi, Tomohiro. "Non-commutative arithmetic-geometric mean inequality." Proceedings of the American Mathematical Society 137, no. 10 (2009): 3399. http://dx.doi.org/10.1090/s0002-9939-09-09911-0.

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9

Lucht, Lutz G. "On the Arithmetic-Geometric Mean Inequality." American Mathematical Monthly 102, no. 8 (1995): 739. http://dx.doi.org/10.2307/2974645.

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10

Eddy, Roland H. "Behold! The Arithmetic-Geometric Mean Inequality." College Mathematics Journal 16, no. 3 (1985): 208. http://dx.doi.org/10.1080/07468342.1985.11972881.

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11

Ando, Tsuyoshi. "Geometric mean and norm Schwarz inequality." Annals of Functional Analysis 7, no. 1 (2016): 1–8. http://dx.doi.org/10.1215/20088752-3158073.

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12

Gilman, Jane. "A geometric approach to Jørgensen's inequality." Advances in Mathematics 85, no. 2 (1991): 193–97. http://dx.doi.org/10.1016/0001-8708(91)90055-c.

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13

Korte, Riikka. "Geometric Implications of the Poincaré Inequality." Results in Mathematics 50, no. 1-2 (2007): 93–107. http://dx.doi.org/10.1007/s00025-006-0237-x.

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14

Lucht, Lutz G. "On the Arithmetic-Geometric Mean Inequality." American Mathematical Monthly 102, no. 8 (1995): 739–40. http://dx.doi.org/10.1080/00029890.1995.12004651.

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15

Hassani, Mehdi. "On the Arithmetic-Geometric mean inequality." Tamkang Journal of Mathematics 44, no. 4 (2013): 453–56. http://dx.doi.org/10.5556/j.tkjm.44.2013.1418.

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16

Fu, Xiaohui. "An operator α-geometric mean inequality". Journal of Mathematical Inequalities, № 3 (2015): 947–50. http://dx.doi.org/10.7153/jmi-09-77.

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17

an Yang, Junj, та Xiaohui Fu. "Squaring operator α-geometric mean inequality". Journal of Mathematical Inequalities, № 2 (2016): 571–75. http://dx.doi.org/10.7153/jmi-10-45.

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18

Hoa, Dinh Trung. "An inequality for t-geometric means." Mathematical Inequalities & Applications, no. 2 (2016): 765–68. http://dx.doi.org/10.7153/mia-19-56.

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19

Audeh, Wasim. "Applications of Arithmetic Geometric Mean Inequality." Advances in Linear Algebra & Matrix Theory 07, no. 02 (2017): 29–36. http://dx.doi.org/10.4236/alamt.2017.72004.

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20

Rosa, Félix Martínez de la. "THE HARMONIC-GEOMETRIC-ARITHMETIC MEAN INEQUALITY." Far East Journal of Mathematical Education 17, no. 1 (2017): 61. http://dx.doi.org/10.17654/me017010061.

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21

Chai, Young Do. "A geometric inequality on mixed volumes." Annals of Global Analysis and Geometry 14, no. 4 (1996): 373–80. http://dx.doi.org/10.1007/bf00129897.

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22

Yun, Zhang. "109.14 Extensions of a Geometric Inequality." Mathematical Gazette 109, no. 574 (2025): 156–59. https://doi.org/10.1017/mag.2025.31.

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23

ROMAN-FLORES, HERIBERTO, and YURILEV CHALCO-CANO. "SUGENO INTEGRAL AND GEOMETRIC INEQUALITIES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, no. 01 (2007): 1–11. http://dx.doi.org/10.1142/s0218488507004340.

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In this work, we prove a Prékopa-Leindler type inequality for the Sugeno integral. More precisely, if 0 < λ < 1 and h((1-λ)x+λy) ≥ f(x)1-λg(y)λ, ∀ x,y ∈ ℝn, where h, f and g are nonnegative μ-measurable functions on ℝn, then [Formula: see text], for any concave fuzzy measure μ. Also, we derive a general Brunn-Minkowski inequality (standard form) for any homogeneous quasiconcave fuzzy measure μ on ℝn.

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24

Zhou, Jiazu. "On Willmore's Inequality for Submanifolds." Canadian Mathematical Bulletin 50, no. 3 (2007): 474–80. http://dx.doi.org/10.4153/cmb-2007-047-4.

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AbstractLet M be an m dimensional submanifold in the Euclidean space Rn and H be the mean curvature ofM. We obtain some low geometric estimates of the total squaremean curvature ∫M H2dσ. The low bounds are geometric invariants involving the volume of M, the total scalar curvature of M, the Euler characteristic and the circumscribed ball of M.

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25

Kwon, E. G. "Extension of Hölder's inequality (I)." Bulletin of the Australian Mathematical Society 51, no. 3 (1995): 369–75. http://dx.doi.org/10.1017/s0004972700014192.

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26

Alzer, Horst. "On Weighted Geometric Means." Canadian Mathematical Bulletin 32, no. 2 (1989): 199–206. http://dx.doi.org/10.4153/cmb-1989-030-4.

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AbstractThe aim of this paper is two-fold: First we prove the Radotype inequality Here denote the weighted geometric means of with where the pi are positive weights. Thereafter we investigate under which conditions the sequence is convergent as n → ∞

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27

Burk, Frank. "The Geometric, Logarithmic, and Arithmetic Mean Inequality." American Mathematical Monthly 94, no. 6 (1987): 527. http://dx.doi.org/10.2307/2322844.

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28

Cannon, James W. "The Cauchy-Schwarz Inequality: A Geometric Proof." American Mathematical Monthly 96, no. 7 (1989): 630. http://dx.doi.org/10.2307/2325185.

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29

Elster, K. H., and R. Elster. "The geometric vector inequality and its properties." Optimization 31, no. 4 (1994): 313–41. http://dx.doi.org/10.1080/02331939408844027.

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30

Bhatia, Rajendra, and Fuad Kittaneh. "The matrix arithmetic–geometric mean inequality revisited." Linear Algebra and its Applications 428, no. 8-9 (2008): 2177–91. http://dx.doi.org/10.1016/j.laa.2007.11.030.

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31

Burk, Frank. "The Geometric, Logarithmic, and Arithmetic Mean Inequality." American Mathematical Monthly 94, no. 6 (1987): 527–28. http://dx.doi.org/10.1080/00029890.1987.12000678.

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32

Cannon, James W. "The Cauchy-Schwarz Inequality: A Geometric Proof." American Mathematical Monthly 96, no. 7 (1989): 630–31. http://dx.doi.org/10.1080/00029890.1989.11972253.

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33

Reznick, Bruce. "Forms derived from the arithmetic-geometric inequality." Mathematische Annalen 283, no. 3 (1989): 431–64. http://dx.doi.org/10.1007/bf01442738.

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34

Fujimoto, Masayuki, and Yuki Seo. "Matrix Richard inequality via the geometric mean." Journal of Mathematical Inequalities, no. 1 (2018): 107–11. http://dx.doi.org/10.7153/jmi-2018-12-08.

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35

Abi-Khuzam, Faruk F. "A trigonometric inequality and its geometric applications." Mathematical Inequalities & Applications, no. 3 (2000): 437–42. http://dx.doi.org/10.7153/mia-03-43.

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36

Zehmisch, Kai. "Lagrangian non-squeezing and a geometric inequality." Mathematische Zeitschrift 277, no. 1-2 (2013): 285–91. http://dx.doi.org/10.1007/s00209-013-1254-6.

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37

Li, Yongtao, Xian-Ming Gu, and Jianxing Zhao. "The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality." Symmetry 10, no. 9 (2018): 380. http://dx.doi.org/10.3390/sym10090380.

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In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

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38

Gao, Peng. "On an inequality of Diananda." International Journal of Mathematics and Mathematical Sciences 2003, no. 32 (2003): 2061–68. http://dx.doi.org/10.1155/s0161171203210279.

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39

Vaziri, Parvaneh, Hadi Khodabakhshian, and Rahim Safshekan. "On convex functions and related inequalities." Annals of the University of Craiova Mathematics and Computer Science Series 50, no. 1 (2023): 91–98. http://dx.doi.org/10.52846/ami.v50i1.1631.

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The main result of this paper is to give refinement and reverse the celebrated Jensen inequality. We directly apply our results to establish several weighted arithmetic-geometric mean inequality. We also present a stronger estimate for the first inequality in the Hermite-Hadamard inequality.

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40

Cai, Jun, and Vladimir Kalashnikov. "NWU property of a class of random sums." Journal of Applied Probability 37, no. 1 (2000): 283–89. http://dx.doi.org/10.1239/jap/1014842286.

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In this note, we derive an inequality for the renewal process. Then, using this inequality, together with an identity in terms of the renewal process for the tails of random sums, we prove that a class of random sums is always new worse than used (NWU). Thus, the well-known NWU property of geometric sums is extended to the class of random sums. This class is illustrated by some examples, including geometric sums, mixed geometric sums, certain mixed Poisson distributions and certain negative binomial sums.

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41

Cai, Jun, and Vladimir Kalashnikov. "NWU property of a class of random sums." Journal of Applied Probability 37, no. 01 (2000): 283–89. http://dx.doi.org/10.1017/s0021900200015436.

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In this note, we derive an inequality for the renewal process. Then, using this inequality, together with an identity in terms of the renewal process for the tails of random sums, we prove that a class of random sums is always new worse than used (NWU). Thus, the well-known NWU property of geometric sums is extended to the class of random sums. This class is illustrated by some examples, including geometric sums, mixed geometric sums, certain mixed Poisson distributions and certain negative binomial sums.

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42

Li, Yanlin, Md Aquib, Meraj Ali Khan, Ibrahim Al-Dayel, and Maged Zakaria Youssef. "Geometric Inequalities of Slant Submanifolds in Locally Metallic Product Space Forms." Axioms 13, no. 7 (2024): 486. http://dx.doi.org/10.3390/axioms13070486.

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In this particular article, our focus revolves around the establishment of a geometric inequality, commonly referred to as Chen’s inequality. We specifically apply this inequality to assess the square norm of the mean curvature vector and the warping function of warped product slant submanifolds. Our investigation takes place within the context of locally metallic product space forms with quarter-symmetric metric connections. Additionally, we delve into the condition that determines when equality is achieved within the inequality. Furthermore, we explore a number of implications of our finding

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43

KAZAZ, MUSTAFA, MOHD ASLAM, and MOHD AQUIB. "Geometric Inequalities for Statistical Submanifolds in Cosymplectic Statistical Manifolds." Kragujevac Journal of Mathematics 48, no. 3 (2024): 393–405. http://dx.doi.org/10.46793/kgjmat2403.393k.

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In this paper, we obtain two important geometric inequalities namely, Euler’s inequality and Chen’s inequality for statistical submanifolds in cosymplectic statistical manifolds with constant curvature, and discuss the equality case of the inequalities. We also give some applications of the inequalities obtained.

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44

Zhang, Teng. "A note on the matrix arithmetic-geometric mean inequality." Electronic Journal of Linear Algebra 34 (February 21, 2018): 283–87. http://dx.doi.org/10.13001/1081-3810.3555.

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This note proves the following inequality: If $n=3k$ for some positive integer $k$, then for any $n$ positive definite matrices $\bA_1,\bA_2,\dots,\bA_n$, the following inequality holds: \begin{equation*}\label{eq:main} \frac{1}{n^3} \, \Big\|\sum_{j_1,j_2,j_3=1}^{n}\bA_{j_1}\bA_{j_2}\bA_{j_3}\Big\| \,\geq\, \frac{(n-3)!}{n!} \, \Big\|\sum_{\substack{j_1,j_2,j_3=1,\\\text{$j_1$, $j_2$, $j_3$ all distinct}}}^{n}\bA_{j_1}\bA_{j_2}\bA_{j_3}\Big\|, \end{equation*} where $\|\cdot\|$ represents the operator norm. This inequality is a special case of a recent conjecture proposed by Recht and R\'{e} (

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45

He, Guoqing, Juan Zhang, and Peibiao Zhao. "Geometric inequalities for non-integrable distributions in statistical manifolds with constant curvature." Filomat 35, no. 11 (2021): 3585–96. http://dx.doi.org/10.2298/fil2111585h.

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In this paper, we make Euler inequality, Chen first inequality and Chen-Ricci inequality for non-integrable distributions in statistical manifolds with constant curvatures. Moreover, we investigate the conditions for equality cases.

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46

Čižmešija, Aleksandra, Josip Pecarić, and Lars–Erik Persson. "On strengthened weighted Carleman's inequality." Bulletin of the Australian Mathematical Society 68, no. 3 (2003): 481–90. http://dx.doi.org/10.1017/s0004972700037886.

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47

Perla, Sreenivasa Reddy, S. Padmanabhan, and V. Lokesha. "Schur Geometric Convexity of Related Function for Holders Inequality with Application." European Journal of Pure and Applied Mathematics 13, no. 5 (2020): 1199–211. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3741.

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48

KONAGA, YU, YUSUKE NISHIZAWA, RYUJI SAITO, and RIKI SATO. "THE ARITHMETIC-GEOMETRIC MEAN INEQUALITY RESULTING FROM THE FUNCTION CONTAINING e x AND x e." Journal of Inequalities and Special Functions 14, no. 3 (2023): 1–6. https://doi.org/10.54379/jiasf-2023-3-1.

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49

Pasteczka, Paweł. "Jensen-type geometric shapes." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19, no. 1 (2020): 27–33. http://dx.doi.org/10.2478/aupcsm-2020-0002.

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AbstractWe present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary.It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.

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50

Ruzhansky, Michael, Bolys Sabitbek, and Durvudkhan Suragan. "Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups." Bulletin of Mathematical Sciences 10, no. 03 (2020): 2050016. http://dx.doi.org/10.1142/s1664360720500162.

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In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: [Formula: see text] which solves a conjecture in the paper [S. Larson, Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domain in the Heisenberg group, Bull. Math. Sci. 6 (2016) 335–352]. Here, [Formula: see text] is the angle function. Also, we obtain a version of the Hardy–Sobolev inequality in a half-space of the Heisenberg grou

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