Geodesic
Applications of the fractional difference operator for studying Euler statistical convergence of sequences of fuzzy real numbers and associated Korovkin-type theorems
Problemy analiza, Tome 11 (2022) no. 3, pp. 91-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

The present work focuses on the statistical Euler summability, Euler statistical convergence, and Euler summability of sequences of fuzzy real numbers via the generalized fractional difference operator. We make an effort to establish some relations between different sorts of Euler convergence. Further, we discuss the fuzzy continuity and demonstrate a fuzzy Korovkin-type approximation theorem. Finally, we study fuzzy rate of the convergence of approximating fuzzy positive linear operators through the modulus of continuity.
Keywords: Euler mean, sequences of fuzzy real numbers, statistical convergence, rate of convergence, approximation theorem. 
@article{PA_2022_11_3_a6,
     author = {Kuldip Raj and Kavita Saini and M. Mursaleen},
     title = {Applications of the fractional difference operator for studying {Euler} statistical convergence of sequences of fuzzy real numbers and associated {Korovkin-type} theorems},
     journal = {Problemy analiza},
     pages = {91--108},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2022_11_3_a6/}
}
TY  - JOUR
AU  - Kuldip Raj
AU  - Kavita Saini
AU  - M. Mursaleen
TI  - Applications of the fractional difference operator for studying Euler statistical convergence of sequences of fuzzy real numbers and associated Korovkin-type theorems
JO  - Problemy analiza
PY  - 2022
SP  - 91
EP  - 108
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2022_11_3_a6/
LA  - en
ID  - PA_2022_11_3_a6
ER  - 
%0 Journal Article
%A Kuldip Raj
%A Kavita Saini
%A M. Mursaleen
%T Applications of the fractional difference operator for studying Euler statistical convergence of sequences of fuzzy real numbers and associated Korovkin-type theorems
%J Problemy analiza
%D 2022
%P 91-108
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2022_11_3_a6/
%G en
%F PA_2022_11_3_a6
Kuldip Raj; Kavita Saini; M. Mursaleen. Applications of the fractional difference operator for studying Euler statistical convergence of sequences of fuzzy real numbers and associated Korovkin-type theorems. Problemy analiza, Tome 11 (2022) no. 3, pp. 91-108. http://geodesic.mathdoc.fr/item/PA_2022_11_3_a6/

[1] Ayman-Mursaleen M., Serra-Capizzano S., “Statistical Convergence via q-Calculus and a Korovkin's Type Approximation Theorem”, Axioms, 11 (2022), 70 | DOI

[2] Aytar S., Mammadov M. A., Pehlivan S., “Statistical limit inferior and limit superior for sequences of fuzzy numbers”, Fuzzy Sets Syst., 157 (2006), 976–985 | DOI | MR | Zbl

[3] Baliarsingh P., “On a fractional difference operator”, Alex. Eng. J., 55 (2016), 1811–1816 | DOI

[4] Baliarsingh P., Kadak U., Mursaleen M., “On statistical convergence of difference sequences of fractional order and related Korovkin type approximation theorems”, Quaest. Math., 41 (2018), 1117–1133 | DOI | MR | Zbl

[5] Connor J., “Two valued measures and summability”, Analysis, 10 (1990), 373–386 | DOI | MR

[6] Çolak R., Alt{\i}n Y., Mursaleen M., “On some sets of difference sequences of fuzzy numbers”, Soft Comput., 15 (2010), 787–793 | DOI

[7] Fast H., “Sur le convergence”, Colloq. Math., 2 (1951), 241–244 | DOI | MR | Zbl

[8] Fridy J. A., “On statistical convergent”, Analysis, 5 (1985), 301–314 | DOI | MR

[9] Gasper G., Rahman M., Basic Hypergeometric Series, Camb. Univ. Press, 2004 | MR | Zbl

[10] Hardy G. H., Divergent Series, Clarendon Press, Oxford, 1949 | MR | Zbl

[11] Kadak U., Mursaleen M., Mohiuddine S. A., “Statistical weighted matrix summability of fuzzy mappings and associated approximation results”, J. Intel. Fuzzy Syst., 36 (2019), 3483–3494 | DOI

[12] Kadak U., Srivastava H. M., Mursaleen M., “Relatively uniform weighted summability based on fractional-order difference operator”, Bull. Malays. Math. Sci. Soc., 42 (2019), 2453–2480 | DOI | MR | Zbl

[13] Miller H. I., Orhan C., “On almost convergent and statistically convergent subsequences”, Acta Math. Hung., 93 (2001), 131–151 | DOI | MR

[14] Mohiuddine S. A., Asiri A., Hazarika B., “Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems”, Int. J. General Syst., 48 (2019), 492–506 | DOI | MR

[15] Mursaleen M., “$\lambda$-statistical convergence”, Math. Slovaca, 50 (2000), 111–115 | MR | Zbl

[16] Mursaleen M., Alotaibi A., “Statistical summability and approximation by de la Vallée-Poussin mean”, Appl. Math. Lett., 24 (2011), 320–324 | DOI | MR | Zbl

[17] Mursaleen M., Alotaibi A., “Korovkin type approximation theorems for functions of two variables through statistical $A$-summability”, Adv. Difference Equ., 2012 (2012), 1–10 | DOI | MR

[18] Mursaleen M., Başar F., Sequence Spaces: Topics in Modern Summability Theory, Mathematics and Its Applications, CRC Press/Taylor $\$ Francis Group, Boca Raton–London–New York, 2020 | Zbl

[19] Patro M., Paikray S. K., Dutta H., “Statistical Deferred Euler Summability Mean and Associated Korovokin-type Approximation Theorem”, Sci. Technol. Asia, 25 (2020), 31–37

[20] Puri M. L., Ralescu D. A., “Differentials of fuzzy functions”, J. Math. Anal. Appl., 91 (1983), 552–558 | DOI | MR | Zbl

[21] Steinhaus H., “Sur la convergence ordinarie et la convergence asymptotique”, Colloq. Math., 2 (1951), 73–74 | DOI | MR

[22] Savaş E., “On statistically convergent sequences of fuzzy numbers”, Inf. Sci., 137 (2001), 277–282 | DOI | MR | Zbl

[23] Talo Ö., Başar F., “Certain spaces of sequences of fuzzy numbers defined by a modulus function”, Demonstratio Math., 43 (2010), 139–149 | DOI | MR | Zbl

[24] Talo Ö., Başar F., “Quasilinearity of the classical sets of sequences of fuzzy numbers and some related results”, Taiwanese J. Math., 14 (2010), 1799–1819 | DOI | MR | Zbl

[25] Tripathy B. C., Baruah A., “New type of difference sequence spaces of fuzzy real numbers”, Math. Modell. Analysis, 14 (2009), 391–397 | DOI | MR | Zbl

[26] Tripathy B. C., Borgogain S., “Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function”, Advances in Fuzzy Systems, 2011, 216414, 6 pp. | MR | Zbl

[27] Zadeh L. A., “Fuzzy sets”, Inform. and Control, 8 (1965), 338–353 | DOI | MR | Zbl