Korovkin type approximation theorem via lacunary equi-statistical convergence in fuzzy spaces

Volume 25, Issue 4, pp 312--321 http://dx.doi.org/10.22436/jmcs.025.04.02

Publication Date: August 09, 2021 Submission Date: May 27, 2021 Revision Date: June 14, 2021 Accteptance Date: June 26, 2021

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 868 Downloads
• 1473 Views

Authors

M. Aiyub - Department of Mathematics, College of Sciences, University of Bahrain, Manama, Kingdom of Bahrain. K. Saini - School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, J \(\&\) K, India. K. Raj - School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, J \(\&\) K, India.

Abstract

In the present paper, we establish relations between equi-statistical convergence and lacunary equi-statistical convergence of sequences of fuzzy number valued functions. We make an effort to prove Korovkin type approximation theorem via lacunary equi-statistical convergence in fuzzy spaces. Further, we study rates of lacunary equi-statistical fuzzy convergence by using fuzzy modulus of continuity.

Share and Cite

Keywords

• Fuzzy number
• lacunary equi-statistical convergence
• fuzzy rate
• fuzzy positive linear operator
• Korovkin type approximation theorem

MSC

•  40A05
•  40A30

References

• [1] H. Aktuglu, H. Gezer, Lacunary equi-statistical convergence of positive linear operators, Cent. Eur. J. Math., 7 (2009), 558--567
  • View Article


• [2] G. A. Anastassiou, On basic fuzzy Korovkin theory, Studia Univ. Babes¸-Bolyai Math., 50 (2005), 3--10
  • View Article


• [3] G. A. Anastassiou, O. Duman, Statistical fuzzy approximation by fuzzy positive linear operators, Comput. Math. Appl., 55 (2008), 573--580
  • View Article


• [4] S. Aytar, M. A. Mammadov, S. Pehlivan, Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Sets and Systems, 157 (2006), 976--985
  • View Article


• [5] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl., 328 (2007), 715--729
  • View Article


• [6] M. Bas¸arir, M. Mursaleen, Some difference sequences spaces of fuzzy numbers, J. Fuzzy Math., 12 (2004), 1--6
  • Google Scholar


• [7] C. Belen, S. A. Mohiuddine, Generalized weighted statistical convergence and application, Appl. Math. Comput, 219 (2013), 9821--9826
  • View Article


• [8] R. Colak, Y. Altin, M. Mursaleen, On some sets of difference sequences of fuzzy numbers, Soft Comput., 15 (2010), 787--793
  • View Article


• [9] J. Connor, Two valued measure and summability, Analysis, 10 (1990), 373--385
  • View Article


• [10] O. H. H. Edely, S. A. Mohiuddine, A. K. Noman, Korovkin type approximation theorem obtained through generalized statistical convergence, Appl. Math. Lett., 23 (2010), 1382--1387
  • View Article


• [11] A. Esi, On Some New Paranormed Sequence Spaces of Fuzzy Numbers Defined By Orlicz Functions and Statistical Convergence, Math. Model. Anal., 11 (2006), 379--388
  • View Article


• [12] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241--244
  • View Article


• [13] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301--313
  • View Article


• [14] B. Hazarika, A. Alotaibi, S. A. Mohiuddine, Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput.,, 24 (2020), 6613--6622
  • View Article


• [15] B. Hazarika, A. Esi, On ideal summability and a Korovkin type approximation Theorem, J. Anal., 27 (2019), 1151--1161
  • View Article


• [16] U. Kadak, S. A. Mohiuddine, Generalized statistically almost convergence based on the difference operator which includes the (p, q)-gamma function and related approximation theorems, Results Math., 73 (2018), 31 pages
  • View Article


• [17] V. Kumar, A. Sharma, K. Kumar, N. Singh, On I-limit points and I-cluster points of sequences of fuzzy numbers, Int. Math. Forum, 2 (2007), 2815--2822
  • View Article


• [18] H. I. Miller, C. Orhan, On almost convergent and statistically convergent subsequences, Acta Math. Hungar., 93 (2001), 131--151
  • View Article


• [19] S. A. Mohiuddine, B. A. S. Alamri, Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM,, 113 (2019), 1955--1973
  • View Article


• [20] S. A. Mohiuddine, A. Asiri, B. Hazarika, Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst., 48 (2019), 492--506
  • View Article


• [21] S. A. Mohiuddine, B. Hazarika, A. Alotaibi, On statistical convergence of double sequences of fuzzy valued functions, J. Intell. Fuzzy Syst., 32 (2017), 4331--4342
  • View Article


• [22] M. Mursaleen, A. Alotaibi, Korovkin type approximation theorems for functions of two variables through statistical Asummability, Adv. Difference Equ., 2012 (2012), 10 pages
  • View Article


• [23] M. Mursaleen, M. Basarir, On some new sequences of fuzzy number, Indian J. Pure Appl. Math., 34 (2003), 1351--1357
  • View Article


• [24] S. Nanda, On sequences of fuzzy number, Fuzzy Sets and Systems, 33 (1989), 123--126
  • View Article


• [25] F. Nuray, E. Savas, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca, 45 (1995), 269--273
  • View Article


• [26] S. K. Paikray, P. Parida, S. A. Mohiuddine, A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems, Eur. J. Pure Appl. Math., 13 (2020), 1212--1230
  • View Article


• [27] M. L. Puri, D. A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl., 91 (1983), 552--558
  • View Article


• [28] K. Raj, C. Sharma, A. Choudhary, Applications of tauberian theorem in Orlicz spaces of double difference sequences of fuzzy numbers, J. Intell. Fuzzy Syst., 35 (2018), 2513--1524
  • View Article


• [29] E. Savas, On statistically convergent sequences of fuzzy numbers, Inform. Sci., 137 (2001), 277--282
  • View Article


• [30] H. Steinhaus, Sur la convergence ordinarie et la convergence asymptotique, Colloq. Math., 2 (1951), 73--74
  • Google Scholar


• [31] N. Subramanian, A.Esi, Rough statistical convergence on triple sequence of random variables in probability, Trans. A. Razmadze Math. Inst., 173 (2019), 111--120
  • View Article


• [32] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338--353
  • MathSciNet