Science Explorer Back to mapMap
Discussion
Topic · Applied Mathematics

Functional Equations Stability Results

Functional Equations Stability Results is a research topic within Applied Mathematics. Science Explorer counts 13k 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 focuses on the stability of functional equations, particularly in the context of mathematical analysis. It explores topics such as Hyers-Ulam stability, functional equations in Banach spaces, stability of linear differential equations, quadratic equations, fixed point approaches, approximate homomorphisms, fuzzy stability, non-Archimedean spaces, and the Pexider equation.

  • Hyers-Ulam Stability
  • Functional Equations
  • Banach Spaces
  • Linear Differential Equations
  • Quadratic Equation
  • Fixed Point Approach
  • Approximate Homomorphisms
  • Fuzzy Stability
  • Non-Archimedean Spaces
  • Pexider Equation
Research works
13k
fractional, since 1950
In the world top 10%
1.3k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+1%
the tick is no change
Largest producer
China
20% of the 10 largest, 2022-now
Functional Equations Stability Results

Which countries lead Functional Equations Stability Results research?

By volume, China and India publish the most (187 and 155 works in 2022-now).

By volume, 2022-now

  1. 1 China 187 works
  2. 2 India 155 works
  3. 3 United States 113 works
  4. 4 Türkiye 89 works
  5. 5 Iran 81 works
  6. 6 Poland 78 works
  7. 7 Saudi Arabia 76 works
  8. 8 Pakistan 66 works
  9. 9 Russia 49 works
  10. 10 Morocco 45 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: 19.9%India: 16.5%United States: 12.0%Türkiye: 9.5%6 others listed: 42.0%20%largest
China187 · 19.9%India155 · 16.5%United States113 · 12.0%Türkiye89 · 9.5%6 others listed395 · 42.0%

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

Which institutions lead Functional Equations Stability Results research?

By volume in 2022-now, Düzce Üniversitesi publishes the most Functional Equations Stability Results research, followed by Islamic Azad University, Tehran and Polish Academy of Sciences.

By volume, 2022-now

  1. 1 Düzce ÜniversitesiTürkiye 24 works
  2. 2 Islamic Azad University, TehranIran 16 works
  3. 3 Polish Academy of SciencesPoland 15 works
  4. 4 COMSATS University IslamabadPakistan 15 works
  5. 5 Centre National de la Recherche ScientifiqueFrance 14 works
  6. 6 Hanyang UniversitySouth Korea 13 works
  7. 7 University of DebrecenHungary 12 works
  8. 8 Russian Academy of SciencesRussia 12 works
  9. 9 University of Mohaghegh ArdabiliIran 12 works
  10. 10 AGH University of KrakowPoland 11 works

Who are the leading researchers in Functional Equations Stability Results?

The most-cited researchers publishing on Functional Equations Stability Results include Guanrong Chen.

  1. 1 Guanrong Chen China 116k 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 Functional Equations Stability Results?

The most cited paper in Functional Equations Stability Results is "On the stability of the linear mapping in Banach spaces" (Themistocles M. Rassias, 1978), with 2,860 citations. Next come "A Course in Functional Analysis." (2,360) and "Mean value methods in iteration" (2,327).

Most cited papers
#PaperReleasedCitations
1 On the stability of the linear mapping in Banach spaces Themistocles M. Rassias · Proceedings of the American Mathematical Society Open access Nov 1978 2,860
2 A Course in Functional Analysis. Theodore W. Gamelin, John B. Conway · American Mathematical Monthly Nov 1986 2,360
3 Mean value methods in iteration W. Robert Mann · Proceedings of the American Mathematical Society Jun 1953 2,327
4 Fuzzy random variables MADAN LAL PURI, Dan A. Ralescu · Journal of Mathematical Analysis and Applications Open access Mar 1986 1,872
5 Fuzzy differential equations Osmo Kaleva · Fuzzy Sets and Systems Dec 1987 1,718
All 99 most cited papers, with filters and sorting

Where is Functional Equations Stability Results research done?

The largest centres of Functional Equations Stability Results research in 2022-now are Tehran (Iran), Seoul (South Korea), Düzce (Türkiye) and Chennai (India). Among places with at least 20 works in it, it is an unusually large share of all research in Düzce.

Largest cities, 2022-now

  1. 1 TehranIran 26 works
  2. 2 SeoulSouth Korea 25 works
  3. 3 DüzceTürkiye 24 works
  4. 4 ChennaiIndia 21 works
  5. 5 MoscowRussia 21 works
  6. 6 KrakowPoland 20 works
  7. 7 RiyadhSaudi Arabia 19 works
  8. 8 WarsawPoland 19 works
  9. 9 IslamabadPakistan 18 works
  10. 10 BeijingChina 15 works

Where it is the local speciality

  1. DüzceTR · 23.9 works92×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Functional Equations Stability Results than the world average.

See Functional Equations Stability Results on the map

Where is the best place to study Functional Equations Stability Results?

Among universities, judged by research, Düzce Üniversitesi, COMSATS University Islamabad and AGH University of Krakow 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 12.34%fractional works in this field (log) →share of work in the world top 10% →COMSATS University I…Düzce ÜniversitesiAGH University of Kr…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
1Düzce ÜniversitesiTürkiye 82.222.2%102.6×24 +17.5%
2COMSATS University IslamabadPakistan 76.328.5%43.3×15 -28.8%
3AGH University of KrakowPoland 54.818.0%19.8×11 +13.4%
4King Abdulaziz UniversitySaudi Arabia 52.513.3%13.3×10 +210.2%
5University of Mohaghegh ArdabiliIran 51.311.5%93.3×12 +36.3%
6Islamic Azad University, TehranIran 46.815.8%6.7×16 -53.7%
7Hanyang UniversitySouth Korea 41.210.5%20.3×13 -33.8%
8University of DebrecenHungary 34.12.9%29.7×12 -1.1%
9University of ZagrebCroatia 30.00.1%9.8×10 +63.3%
10King Faisal UniversitySaudi Arabia 28.70.6%22.6×8 +264.0%

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 Functional Equations Stability Results, country by country

Is Functional Equations Stability Results research growing?

Output in 2022-2025 was 1% higher than in 2018-2021, peaking in 2011. The fastest-growing topics are Functional Equations Stability Results.

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 Functional Equations Stability Results as a percentage of every work published that year, 0.0071% in 2024.

still counting0.020%0.040%0.060%Functional Equations Stability Results0.0069% in 202519801990200020102020

Fractional works of Functional Equations Stability Results 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%Functional Equations Stability Results10.0% 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 Functional Equations Stability Results. Posts are plain text and can be reported.