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Topic · Applied Mathematics

Mathematical Inequalities and Applications

Mathematical Inequalities and Applications is a research topic within Applied Mathematics. Science Explorer counts 8.9k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores matrix inequalities, geometric means, fractional integrals, Hermite-Hadamard inequalities, convex functions, Riemannian geometry, quantum calculus, complete monotonicity, operator inequalities, and the gamma function.

  • Matrix Inequalities
  • Geometric Means
  • Fractional Integrals
  • Hermite-Hadamard Inequalities
  • Convex Functions
  • Riemannian Geometry
  • Quantum Calculus
  • Complete Monotonicity
  • Operator Inequalities
  • Gamma Function
Research works
8.9k
fractional, since 1950
In the world top 10%
890
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+2%
the tick is no change
Largest producer
China
23% of the 10 largest, 2022-now
Mathematical Inequalities and Applications

Which countries lead Mathematical Inequalities and Applications research?

By volume, China and Türkiye publish the most (267 and 167 works in 2022-now).

By volume, 2022-now

  1. 1 China 267 works
  2. 2 Türkiye 167 works
  3. 3 India 167 works
  4. 4 Pakistan 135 works
  5. 5 Saudi Arabia 105 works
  6. 6 United States 97 works
  7. 7 Jordan 59 works
  8. 8 Iran 59 works
  9. 9 France 50 works
  10. 10 Romania 46 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 23.2%Türkiye: 14.5%India: 14.5%Pakistan: 11.7%6 others listed: 36.1%23%largest
China267 · 23.2%Türkiye167 · 14.5%India167 · 14.5%Pakistan135 · 11.7%6 others listed416 · 36.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead Mathematical Inequalities and Applications research?

By volume in 2022-now, Düzce Üniversitesi publishes the most Mathematical Inequalities and Applications research, followed by COMSATS University Islamabad and Université de Caen Normandie.

By volume, 2022-now

  1. 1 Düzce ÜniversitesiTürkiye 51 works
  2. 2 COMSATS University IslamabadPakistan 34 works
  3. 3 Université de Caen NormandieFrance 21 works
  4. 4 Victoria UniversityAustralia 19 works
  5. 5 University of SargodhaPakistan 17 works
  6. 6 University of ZagrebCroatia 17 works
  7. 7 King Saud UniversitySaudi Arabia 16 works
  8. 8 University of JordanJordan 14 works
  9. 9 China Three Gorges UniversityChina 13 works
  10. 10 University of GuelmaAlgeria 12 works

Who are the leading researchers in Mathematical Inequalities and Applications?

The most-cited researchers publishing on Mathematical Inequalities and Applications include Peter M. Bentler, James J. Heckman and John A. Todd.

  1. 1 Peter M. Bentler United States 233k citations
  2. 2 James J. Heckman United States 122k citations
  3. 3 John A. Todd United Kingdom 107k citations
  4. 4 Gene Howard Golub United States 89k citations
  5. 5 Dumitru Bǎleanu Türkiye 89k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Mathematical Inequalities and Applications?

The most cited paper in Mathematical Inequalities and Applications is "Robust principal component analysis?" (Emmanuel J. Candès, Xiaodong Li, Yi Ma et al., 2011), with 6,962 citations. Next come "On certain integrals of Lipschitz-Hankel type involving products of bessel functions" (4,401) and "On Nonlinear Fractional Programming" (3,205).

Most cited papers
#PaperReleasedCitations
1 Robust principal component analysis? Emmanuel J. Candès, Xiaodong Li, Yi Ma et al. · Journal of the ACM May 2011 6,962
2 On certain integrals of Lipschitz-Hankel type involving products of bessel functions G. Eason, Ben Noble, Ian Naismith Sneddon · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences 19 Apr 1955 4,401
3 On Nonlinear Fractional Programming Werner Dinkelbach · Management Science Mar 1967 3,205
4 Generalized reduced rank tests using the singular value decomposition Frank R. Kleibergen, Richard Paap · Journal of Econometrics 5 May 2005 2,775
5 Rényi Divergence and Kullback-Leibler Divergence Tim van Erven, Peter Harremoës · IEEE Transactions on Information Theory Open access 19 Jun 2014 1,598
All 100 most cited papers, with filters and sorting

Where is Mathematical Inequalities and Applications research done?

The largest centres of Mathematical Inequalities and Applications research in 2022-now are Düzce (Türkiye), Islamabad (Pakistan), Riyadh (Saudi Arabia) and Amman (Jordan). Among places with at least 20 works in it, it is an unusually large share of all research in Düzce and Caen.

Largest cities, 2022-now

  1. 1 DüzceTürkiye 51 works
  2. 2 IslamabadPakistan 41 works
  3. 3 RiyadhSaudi Arabia 36 works
  4. 4 AmmanJordan 33 works
  5. 5 CaenFrance 29 works
  6. 6 HangzhouChina 24 works
  7. 7 MelbourneAustralia 22 works
  8. 8 NanjingChina 20 works
  9. 9 ZagrebCroatia 19 works
  10. 10 BeijingChina 19 works

Where it is the local speciality

  1. DüzceTR · 50.5 works181×
  2. CaenFR · 29.1 works62×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Mathematical Inequalities and Applications than the world average.

See Mathematical Inequalities and Applications on the map

Where is the best place to study Mathematical Inequalities and Applications?

Among universities, judged by research, Düzce Üniversitesi, China Three Gorges University and COMSATS University Islamabad score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%25%50%75%mean 23.15%fractional works in this field (log) →share of work in the world top 10% →China Three Gorges U…University of JordanCOMSATS University I…Düzce Üniversitesi
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Düzce ÜniversitesiTürkiye 64.518.6%201.2×50 +30.3%
2China Three Gorges UniversityChina 59.561.1%40.0×13 -14.9%
3COMSATS University IslamabadPakistan 56.021.4%94.5×34 -41.7%
4University of JordanJordan 54.722.3%33.6×14 +266.8%
5University of GuelmaAlgeria 48.831.2%224.7×12 +57.6%
6University of SargodhaPakistan 48.115.0%97.2×17 +59.2%
7King Saud UniversitySaudi Arabia 48.010.4%10.6×16 +185.4%
8Nanjing Normal UniversityChina 46.029.2%17.4×10 +49.0%
9King Khalid UniversitySaudi Arabia 41.716.3%14.0×8 +455.6%
10Université de Caen NormandieFrance 40.56.0%78.2×21 +1092.4%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Mathematical Inequalities and Applications, country by country

Is Mathematical Inequalities and Applications research growing?

Output in 2022-2025 was 2% higher than in 2018-2021, peaking in 2020. The fastest-growing topics are Mathematical Inequalities and Applications.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Mathematical Inequalities and Applications as a percentage of every work published that year, 0.0067% in 2024.

still counting0.0050%0.010%0.015%Mathematical Inequalities and Applications0.0075% in 202519801990200020102020

Fractional works of Mathematical Inequalities and Applications over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Mathematical Inequalities and Applications10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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