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Topic · Geometry and Topology

Fixed Point Theorems Analysis

Fixed Point Theorems Analysis is a research topic within Geometry and Topology. Science Explorer counts 18k 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 fixed point theorems in metric spaces, focusing on contractive mappings, partial ordering, generalized contractions, best proximity points, cone metric spaces, multi-valued mappings, fuzzy metric spaces, and their applications to ordinary differential equations.

  • Fixed Point Theorems
  • Metric Spaces
  • Contractive Mappings
  • Partial Ordering
  • Generalized Contractions
  • Best Proximity Points
  • Cone Metric Spaces
  • Multi-valued Mappings
  • Fuzzy Metric Spaces
  • Ordinary Differential Equations
Research works
18k
fractional, since 1950
In the world top 10%
1.8k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-9%
the tick is no change
Largest producer
India
37% of the 10 largest, 2022-now
Fixed Point Theorems Analysis

Which countries lead Fixed Point Theorems Analysis research?

By volume, India and Saudi Arabia publish the most (810 and 266 works in 2022-now).

By volume, 2022-now

  1. 1 India 810 works
  2. 2 Saudi Arabia 266 works
  3. 3 Türkiye 254 works
  4. 4 China 251 works
  5. 5 Pakistan 142 works
  6. 6 Iran 115 works
  7. 7 Iraq 113 works
  8. 8 United States 90 works
  9. 9 Romania 83 works
  10. 10 South Africa 78 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.

India: 36.8%Saudi Arabia: 12.1%Türkiye: 11.5%China: 11.4%6 others listed: 28.2%37%largest
India810 · 36.8%Saudi Arabia266 · 12.1%Türkiye254 · 11.5%China251 · 11.4%6 others listed621 · 28.2%

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

Which institutions lead Fixed Point Theorems Analysis research?

By volume in 2022-now, King Abdulaziz University publishes the most Fixed Point Theorems Analysis research, followed by Prince Sultan University and Islamic Azad University, Tehran.

By volume, 2022-now

  1. 1 King Abdulaziz UniversitySaudi Arabia 53 works
  2. 2 Prince Sultan UniversitySaudi Arabia 37 works
  3. 3 Islamic Azad University, TehranIran 30 works
  4. 4 University of BelgradeSerbia 30 works
  5. 5 University of JeddahSaudi Arabia 29 works
  6. 6 Aligarh Muslim UniversityIndia 29 works
  7. 7 Osmania UniversityIndia 29 works
  8. 8 China Medical UniversityTaiwan 28 works
  9. 9 Technion – Israel Institute of TechnologyIsrael 27 works
  10. 10 International Islamic University, IslamabadPakistan 26 works

Who are the leading researchers in Fixed Point Theorems Analysis?

The most-cited researchers publishing on Fixed Point Theorems Analysis include Guanrong Chen, Dumitru Bǎleanu and Terence Tao.

  1. 1 Guanrong Chen China 116k citations
  2. 2 Dumitru Bǎleanu Türkiye 89k citations
  3. 3 Terence Tao United States 78k citations
  4. 4 Robert W. Heath United States 77k citations
  5. 5 Dimitri P. Bertsekas United States 73k 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 Fixed Point Theorems Analysis?

The most cited paper in Fixed Point Theorems Analysis is "Multi-valued contraction mappings" (Sam B. Nadler, 1969), with 2,362 citations. Next come "Iterative Algorithms for Nonlinear Operators" (1,676) and "Various generalizations of metric spaces and fixed point theorems" (1,588).

Most cited papers
#PaperReleasedCitations
1 Multi-valued contraction mappings Sam B. Nadler · Pacific Journal of Mathematics Open access Aug 1969 2,362
2 Iterative Algorithms for Nonlinear Operators Hong‐Kun Xu · Journal of the London Mathematical Society Aug 2002 1,676
3 Various generalizations of metric spaces and fixed point theorems Tran Van An, Nguyen Van Dũng, Zoran Kadelburg et al. · Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas 12 Jun 2014 1,588
4 On some results in fuzzy metric spaces Aravind George, P. Veeramani · Fuzzy Sets and Systems Jun 1994 1,575
5 A fixed point theorem in partially ordered sets and some applications to matrix equations André C. M. Ran, Martine Reurings · Proceedings of the American Mathematical Society Open access 18 Sep 2003 1,426
All 100 most cited papers, with filters and sorting

Where is Fixed Point Theorems Analysis research done?

The largest centres of Fixed Point Theorems Analysis research in 2022-now are Jeddah (Saudi Arabia), Riyadh (Saudi Arabia), Islamabad (Pakistan) and Chennai (India). Among places with at least 20 works in it, it is an unusually large share of all research in Lahore, Beni Mellal and Tabuk.

Largest cities, 2022-now

  1. 1 JeddahSaudi Arabia 83 works
  2. 2 RiyadhSaudi Arabia 73 works
  3. 3 IslamabadPakistan 50 works
  4. 4 ChennaiIndia 49 works
  5. 5 BaghdadIraq 47 works
  6. 6 TaichungTaiwan 45 works
  7. 7 AnkaraTürkiye 38 works
  8. 8 HyderabadIndia 36 works
  9. 9 PretoriaSouth Africa 36 works
  10. 10 BelgradeSerbia 34 works

Where it is the local speciality

  1. LahorePK · 22.7 works77×
  2. Beni MellalMA · 26.0 works56×
  3. TabukSA · 24.5 works50×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Fixed Point Theorems Analysis than the world average.

See Fixed Point Theorems Analysis on the map

Where is the best place to study Fixed Point Theorems Analysis?

Among universities, judged by research, Prince Sultan University, University of Tabuk and King Abdulaziz University 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%10%20%30%mean 20.94%fractional works in this field (log) →share of work in the world top 10% →University of BelgradeUniversity of TabukPrince Sultan Univer…King Abdulaziz Unive…
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
1Prince Sultan UniversitySaudi Arabia 82.720.5%116.1×37 +8.4%
2University of TabukSaudi Arabia 81.724.6%61.4×24 +1014.1%
3King Abdulaziz UniversitySaudi Arabia 79.813.0%33.5×53 +46.6%
4University of BelgradeSerbia 73.025.6%15.2×30 -16.4%
5China Medical UniversityTaiwan 72.721.0%70.5×28 -55.7%
6Government College University, LahorePakistan 72.527.1%62.3×17 +55.4%
7University of Management and TechnologyPakistan 70.417.3%82.2×23 +142.7%
8Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 67.921.8%22.2×17 +108.2%
9Université Sultan Moulay SlimaneMorocco 66.214.4%65.5×26 +45.9%
10Universitat Politècnica de ValènciaSpain 65.324.1%14.3×15 +6.3%

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 Fixed Point Theorems Analysis, country by country

Is Fixed Point Theorems Analysis research growing?

Output in 2022-2025 was 9% lower than in 2018-2021, peaking in 2021.

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 Fixed Point Theorems Analysis as a percentage of every work published that year, 0.012% in 2024.

still counting0.010%0.020%0.030%Fixed Point Theorems Analysis0.013% in 202519801990200020102020

Fractional works of Fixed Point Theorems Analysis 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%Fixed Point Theorems Analysis10.1% 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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