Science Explorer Back to mapMap
Discussion
Topic · Statistics and Probability

Approximation Theory and Sequence Spaces

Approximation Theory and Sequence Spaces is a research topic within Statistics and Probability. Science Explorer counts 12k 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 statistical convergence in approximation theory, functional analysis, and sequence spaces. It covers topics such as approximation theorems, double sequences, Bernstein polynomials, ideal convergence, and summability methods. The research also delves into applications in Orlicz spaces and Kantorovich operators.

  • Statistical Convergence
  • Approximation Theorems
  • Double Sequences
  • Bernstein Polynomials
  • Sequence Spaces
  • Ideal Convergence
  • Summability Methods
  • Kantorovich Operators
  • Orlicz Spaces
  • Functional Analysis
Research works
12k
fractional, since 1950
In the world top 10%
1.2k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+11%
the tick is no change
Largest producer
India
28% of the 10 largest, 2022-now
Approximation Theory and Sequence Spaces

Which countries lead Approximation Theory and Sequence Spaces research?

By volume, India and Türkiye publish the most (348 and 325 works in 2022-now).

By volume, 2022-now

  1. 1 India 348 works
  2. 2 Türkiye 325 works
  3. 3 China 138 works
  4. 4 United States 105 works
  5. 5 Russia 92 works
  6. 6 Iraq 57 works
  7. 7 Spain 54 works
  8. 8 Saudi Arabia 51 works
  9. 9 Romania 46 works
  10. 10 Italy 44 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: 27.7%Türkiye: 25.8%China: 11.0%United States: 8.3%6 others listed: 27.2%28%largest
India348 · 27.7%Türkiye325 · 25.8%China138 · 11.0%United States105 · 8.3%6 others listed343 · 27.2%

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

Which institutions lead Approximation Theory and Sequence Spaces research?

By volume in 2022-now, Tripura University publishes the most Approximation Theory and Sequence Spaces research, followed by Russian Academy of Sciences and University of Memphis.

By volume, 2022-now

  1. 1 Tripura UniversityIndia 23 works
  2. 2 Russian Academy of SciencesRussia 20 works
  3. 3 University of MemphisUnited States 18 works
  4. 4 Aligarh Muslim UniversityIndia 17 works
  5. 5 Chandigarh UniversityIndia 16 works
  6. 6 Netaji Subhas University of TechnologyIndia 16 works
  7. 7 Lomonosov Moscow State UniversityRussia 15 works
  8. 8 Gazi UniversityTürkiye 15 works
  9. 9 Bartin UniversityTürkiye 14 works
  10. 10 Fırat UniversityTürkiye 13 works

Who are the leading researchers in Approximation Theory and Sequence Spaces?

The most-cited researchers publishing on Approximation Theory and Sequence Spaces include Sudhir Kumar, R. W. L. Jones and Guanrong Chen.

  1. 1 Sudhir Kumar United States 295k citations
  2. 2 R. W. L. Jones United Kingdom 189k citations
  3. 3 Guanrong Chen China 116k citations
  4. 4 John A. Todd United Kingdom 107k 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 Approximation Theory and Sequence Spaces?

The most cited paper in Approximation Theory and Sequence Spaces is "Convergence of Probability Measures" (James L. Snell, 1970), with 1,379 citations. Next come "Some results on Tchebycheffian spline functions" (1,266) and "On convergence and growth of partial sums of Fourier series" (1,022).

Most cited papers
#PaperReleasedCitations
1 Convergence of Probability Measures James L. Snell · Technometrics Feb 1970 1,379
2 Some results on Tchebycheffian spline functions George Kimeldorf, Grace Wahba · Journal of Mathematical Analysis and Applications Open access 1971 1,266
3 On convergence and growth of partial sums of Fourier series Lennart Carleson · Acta Mathematica Open access 1966 1,022
4 Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence Pu Pao-Ming, Liu Ying-ming · Journal of Mathematical Analysis and Applications Open access Aug 1980 995
5 Means of positive linear operators Fumio Kubo, Tsuyoshi Andô · Mathematische Annalen Oct 1980 919
All 100 most cited papers, with filters and sorting

Where is Approximation Theory and Sequence Spaces research done?

The largest centres of Approximation Theory and Sequence Spaces research in 2022-now are Ankara (Türkiye), Moscow (Russia), New Delhi (India) and Agartala (India). Among places with at least 20 works in it, it is an unusually large share of all research in Agartala.

Largest cities, 2022-now

  1. 1 AnkaraTürkiye 59 works
  2. 2 MoscowRussia 36 works
  3. 3 New DelhiIndia 34 works
  4. 4 AgartalaIndia 26 works
  5. 5 IstanbulTürkiye 23 works
  6. 6 MemphisUnited States 19 works
  7. 7 TaichungTaiwan 18 works
  8. 8 AligarhIndia 17 works
  9. 9 MohaliIndia 16 works
  10. 10 KyivUkraine 16 works

Where it is the local speciality

  1. AgartalaIN · 25.8 works108×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Approximation Theory and Sequence Spaces than the world average.

See Approximation Theory and Sequence Spaces on the map

Where is the best place to study Approximation Theory and Sequence Spaces?

Among universities, judged by research, University of Perugia, King Abdulaziz University and Tripura 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%20%40%60%mean 24.68%fractional works in this field (log) →share of work in the world top 10% →University of PerugiaKing Abdulaziz Unive…Netaji Subhas Univer…Tripura University
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
1University of PerugiaItaly 70.149.4%28.6×11 +8.4%
2King Abdulaziz UniversitySaudi Arabia 64.842.7%10.2×9 -1.3%
3Tripura UniversityIndia 64.310.9%336.7×24 +55.5%
4Netaji Subhas University of TechnologyIndia 62.929.3%95.1×16 +12.9%
5China Medical UniversityTaiwan 58.725.5%38.2×9 +12.7%
6Gazi UniversityTürkiye 55.215.8%19.6×15 +22.5%
7Chandigarh UniversityIndia 55.118.1%17.9×16 -
8Aligarh Muslim UniversityIndia 54.017.3%34.5×17 -31.0%
9Lomonosov Moscow State UniversityRussia 53.59.3%11.0×16 +30.3%
10Düzce ÜniversitesiTürkiye 46.128.5%33.5×9 -46.1%

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 Approximation Theory and Sequence Spaces, country by country

Is Approximation Theory and Sequence Spaces research growing?

Output in 2022-2025 was 11% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Approximation Theory and Sequence Spaces.

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 Approximation Theory and Sequence Spaces as a percentage of every work published that year, 0.0080% in 2024.

still counting0.020%0.040%Approximation Theory and Sequence Spaces0.0084% in 202519801990200020102020

Fractional works of Approximation Theory and Sequence Spaces 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%Approximation Theory and Sequence Spaces10.0% 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.

Discussion

Ask a question or share a note about Approximation Theory and Sequence Spaces. Posts are plain text and can be reported.