Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Soft Computing
Published in: Soft Computing 11/2021

26-03-2021 | Methodologies and Application

Weighted (λ,μ)-statistical convergence and statistical summability methods of double sequences of fuzzy numbers with application to Korovkin-type fuzzy approximation theorem

Authors: Jyotishmaan Gogoi, Hemen Dutta

Published in: Soft Computing | Issue 11/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The paper aims to investigate different types of weighted statistical convergence and weighted statistical summability of double sequences of fuzzy numbers. Relations connecting statistical convergence and statistical summability have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. Relevant inclusion relations and related results concerning the new fuzzy summability methods have also been examined in detail. Finally, a Korovkin-type approximation theorem for double sequences of fuzzy positive linear operators has been established using the most generalized version of the summability method and showed its efficiency by means of a concrete example.
previous article Collaborative coding and dictionary learning for nearest subspace classification
next article A biometric cryptosystem scheme based on random projection and neural network

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
Alijani Z, Baleanu D, Shiri B, Wu G-C (2020) Spline collocation methods for systems of fuzzy fractional differential equations. Chaos Solitons Fract 131:12MathSciNetCrossRef
Altin Y, Mursaleen M, Altinok H (2010) Statistical summability (C,1)- for sequences of fuzzy real numbers and a Tauberian theorem. J Intell Fuzzy Syst 21:379–384MathSciNetCrossRef
Anastassiou GA, Duman O (2008) Statistical fuzzy approximation by fuzzy positive linear operators. Comput Math Appl 55:573–580MathSciNetCrossRef
Aytar S, Mammadov M, Pehlivan S (2006) Statistical limit inferior and limit superior for sequences of fuzzy numbers. Fuzzy Sets Syst 157:976–985MathSciNetCrossRef
Balen C, Mohiuddine SA (2013) Generalized weighted statistical convergence and application. Appl Math Comput 219:9821–9826MathSciNetMATH
Çanak I (2014) Tauberian theorems for Cesàro summability of sequences of fuzzy numbers. J Intell Fuzzy Syst 27(2):937–942CrossRef
Çanak I, Totur Ü, Önder Z (2017) A Tauberian theorem for (C,1,1) summable double sequences of fuzzy numbers. Iran J Fuzzy Syst 14(1):61–75MathSciNetMATH
Cinar M, Et M (2016) Generalized weighted statistical convergence of double sequences and applications. Filomat 30(3):753–762MathSciNetCrossRef
Coroianu L, Gal SG, Bede B (2014) Approximation of fuzzy numbers by max-product Bernstein operators. Fuzzy Sets Syst 257:41–66MathSciNetCrossRef
Demirci K, Karakuş S (2013) Four-dimensional matrix transformation and A-statistical fuzzy Korovkin type approximation. Demonstratio Math XLVI 2013(1):37–49MathSciNetMATH
Duman O (2010) Statistical fuzzy approximation to fuzzy differentiable functions by fuzzy linear operators. Hacettepe J Math Stat 39(4):497–514MathSciNetMATH
Dutta H, Gogoi J (2019) Weighted λ-statistical convergence connecting a statistical summability of sequences of fuzzy numbers and Korovkin-type approximation theorems. Soft Comput 23:12883–12895CrossRef
Gumah G, Al-Omari S, Baleanu D (2020) Soft computing technique for a system of fuzzy Volterra integro-differential equations in a Hilbert space. Appl Numer Math 152:310–322MathSciNetCrossRef
Karaisa A, Kadak U (2017) On αβ- statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem. Filomat 31(12):3749–3760MathSciNetCrossRef
Kwon JS (2000) On statistical and p- Cesàro convergence of fuzzy numbers. Korean J Comput Appl Math 7(1):195–203MathSciNetCrossRef
Matloka H (1986) Sequences of fuzzy numbers. BUSEFAL 28:28–37MATH
Mursaleen M, Karakaya V, Ertürk M, Gürsoy F (2012) Weighted statistical convergence and its application to Korovkin type approximation theorem. Appl Math Comput 218:9132–9137MathSciNetMATH
Nuray F, Savaş E (1995) Statistical convergence of sequences of fuzzy numbers. MathematicaSlovaka 45(3):269–273MathSciNetMATH
Savaş E, Mursaleen M (2004) On statistically convergent double sequences of fuzzy numbers. Inf Sci 162(3–4):183–192MathSciNetCrossRef
Schoenberg IJ (1959) The integrability of certain functions and related summability methods. Am Math Mon 66:361–375MathSciNetCrossRef
Talo Ö, Başar F (2009) Determination of duals of classical sets of sequences of fuzzy numbers and related matrix transformations. Comput Math Appl 58:717–733MathSciNetCrossRef
Zygmund A (1979) Trigonometric series. Cambridge University Press, CambridgeMATH
Metadata
Title
Weighted (λ,μ)-statistical convergence and statistical summability methods of double sequences of fuzzy numbers with application to Korovkin-type fuzzy approximation theorem
Authors
Jyotishmaan Gogoi
Hemen Dutta
Publication date
26-03-2021
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 11/2021
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-021-05724-2

Other articles of this Issue 11/2021

Soft Computing 11/2021 Go to the issue

Methodologies and Application

Fuzzy C-means robust algorithm for nonlinear systems

Foundations

Filter theory on hyper equality algebras

Methodologies and Application

Resource allocation with advance reservation using artificial neural network in elastic optical networks

Methodologies and Application

Collaborative coding and dictionary learning for nearest subspace classification

Methodologies and Application

Trust-based decision-making framework for multiagent system

Methodologies and Application

Fuzzy-based approaches for agri-food supply chains: a mini-review

Premium Partner

    Image Credits