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Yıl 2020, Cilt: 8 Sayı: 2, 252 - 262, 27.10.2020

Ömer Kişi Erdinç Dündar

Öz

Kaynakça

  • [1] Altin Y., Et M. and Tripathy B.C., On pointwise statistical convergence sequences of fuzzy mappings, J. Fuzzy Math. 15(2) (2007), 425-433.
  • [2] Altinok H., Altin Y., Işık M., Statistical convergence and strong p-Ces`aro summability of order b in sequences of fuzzy numbers, Iran J. Fuzzy Syst. 9(2) (2012), 65-75.
  • [3] Altinok H., Et M., Statistical convergence of order (b; g) for sequences of fuzzy numbers, Soft Computing, 23 (2019), 6017-6022.
  • [4] Aytar S., Pehlivan S., Statistical convergence of sequences of fuzzy numbers and sequences of a-cuts, Inter. J. General Systems, 37(2) (2008), 231-237.
  • [5] Aytar S., Mammadov M.A., Pehlivan S., Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Sets Syst. 157(1) (2006), 976-985.
  • [6] Balcerzak M., Dems K., Komisarski A., Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007), 715-729.
  • [7] Belen C., Mohiuddine SA., Generalized weighted statistical convergence and application, Appl. Math. Comput. 219 (2013), 9821-9826.
  • [8] Çınar M., Karakas¸ M., Et M., On pointwise and uniform statistical convergence of order a for sequences of functions, Fixed Point Theory Appl. 2013:33 (2013), 11 pages, DOI: 10.1186/1687-1812-2013-33
  • [9] Duman O., Orhan C., m-Statistically convergent function sequences, Czech. Math. J. 54(129) (2004), 413-422.
  • [10] Fast H., Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  • [11] Fridy, J.A., On statistical convergence, Analysis, 5 (1985), 301-313.
  • [12] J. A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160(1) (1993), 43-51.
  • [13] Gong Z., Zhang L., Zhu X., The statistical convergence for sequences of fuzzy-number-valued functions, Inf. Sci. 295 (2015), 182-195.
  • [14] Hazarika B., Alotaibi A., Mohiuddine S.A., Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Computing, 24 (2020), 6613-6622.
  • [15] Kadak U., Mohiuddine S. A., Generalized statistically almost convergence based on the difference operator which includes the (p;q)-gamma function and related approximation theorems, Results in Mathematics, 73(1) (2018), Article 9.
  • [16] 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.
  • [17] Kim YK., Ghil BM., Integrals of fuzzy-number-valued functions, Fuzzy Sets Syst. 86 (1997), 213-222.
  • [18] Matloka M., Sequences of fuzzy numbers, Busefal, 28 (1986), 28-37.
  • [19] Nanda S., On sequences of fuzzy numbers, Fuzzy Sets Systems, 33 (1989), 123-126.
  • [20] Mohiuddine SA, Alamri BAS., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matem´aticas RACSAM 113(3) (2019), 1955-1973.
  • [21] Mohiuddine SA., Asiri A., Hazarika B., Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst. 48(5) (2019), 492-506.
  • [22] Mohiuddine S.A. Statistical weighted A-summability with application to Korovkin’s type approximation theorem, J. Inequal. Appl. 2016(101) (2016), https://doi.org/10.1186/s13660-016-1040-1
  • [23] Negoita CV., Ralescu D., Applications of fuzzy sets to systems analysis, (1975), Wiley, New York
  • [24] Nuray F, Savaş E., Statistical convergence of sequences of fuzzy numbers, Math Slovaca, 45(3) (1995), 269-273.
  • [25] Nuray F., Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets and Systems, 99 (1998) 353-355.
  • [26] Salat T., On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.
  • [27] Savas¸ E., On statistically convergent sequences of fuzzy numbers, Inform. Sci. 137(1-4) (2001), 277-282.
  • [28] Schoenberg IJ., The integrability of certain functions and related summability methods, Am. Math. Monthly, 66 (1959), 361-375.
  • [29] Şençimen, C., Pehlivan, S., Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems, 159 (2008), 361-370.
  • [30] Türkmen M.R., Çınar M., Lacunary-statistical convergence in fuzzy normed linear spaces, Appl. Comp. Math. 6(5) (2017), 233-237.
  • [31] Türkmen M.R., Dündar E., On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces, J. Intel. Fuzzy Syst. 36(2) (2019), 1683-1690.
  • [32] Ulusu U., Nuray F., Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics, 4(2) (2012), 99-109.
  • [33] Ulusu U., Dündar E., I-lacunary statistical convergence of sequences of sets, Filomat, 28(8) (2014), 1567-1574.
  • [34] Ulusu U., Nuray F., Lacunary statistical summability of sequences of sets, Konuralp Journal of Mathematics, 3(2) (2015), 176-184.
  • [35] Zadeh L.A., Fuzzy sets, Inform. Control, 8 (1965), 338-353.

Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions

Yıl 2020, Cilt: 8 Sayı: 2, 252 - 262, 27.10.2020

Ömer Kişi Erdinç Dündar

Öz

In this study, we examine the concepts of outer and inner lacunary statistical convergence in measure for sequences of fuzzy-valued measurable functions and show that both kinds of convergence are equivalent in a finite measurable set. Also, we investigate the notion of lacunary statistical convergence in measure for sequences of fuzzy-valued measurable functions and establish interesting results. Furthermore, we give the lacunary statistical version of Egorov's theorem for sequences of fuzzy-valued measurable functions in a finite measurable space.

Anahtar Kelimeler

Pointwise convergence Uniformly convergence Lacunary convergence Fuzzy-valued function

Kaynakça

  • [1] Altin Y., Et M. and Tripathy B.C., On pointwise statistical convergence sequences of fuzzy mappings, J. Fuzzy Math. 15(2) (2007), 425-433.
  • [2] Altinok H., Altin Y., Işık M., Statistical convergence and strong p-Ces`aro summability of order b in sequences of fuzzy numbers, Iran J. Fuzzy Syst. 9(2) (2012), 65-75.
  • [3] Altinok H., Et M., Statistical convergence of order (b; g) for sequences of fuzzy numbers, Soft Computing, 23 (2019), 6017-6022.
  • [4] Aytar S., Pehlivan S., Statistical convergence of sequences of fuzzy numbers and sequences of a-cuts, Inter. J. General Systems, 37(2) (2008), 231-237.
  • [5] Aytar S., Mammadov M.A., Pehlivan S., Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Sets Syst. 157(1) (2006), 976-985.
  • [6] Balcerzak M., Dems K., Komisarski A., Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007), 715-729.
  • [7] Belen C., Mohiuddine SA., Generalized weighted statistical convergence and application, Appl. Math. Comput. 219 (2013), 9821-9826.
  • [8] Çınar M., Karakas¸ M., Et M., On pointwise and uniform statistical convergence of order a for sequences of functions, Fixed Point Theory Appl. 2013:33 (2013), 11 pages, DOI: 10.1186/1687-1812-2013-33
  • [9] Duman O., Orhan C., m-Statistically convergent function sequences, Czech. Math. J. 54(129) (2004), 413-422.
  • [10] Fast H., Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  • [11] Fridy, J.A., On statistical convergence, Analysis, 5 (1985), 301-313.
  • [12] J. A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160(1) (1993), 43-51.
  • [13] Gong Z., Zhang L., Zhu X., The statistical convergence for sequences of fuzzy-number-valued functions, Inf. Sci. 295 (2015), 182-195.
  • [14] Hazarika B., Alotaibi A., Mohiuddine S.A., Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Computing, 24 (2020), 6613-6622.
  • [15] Kadak U., Mohiuddine S. A., Generalized statistically almost convergence based on the difference operator which includes the (p;q)-gamma function and related approximation theorems, Results in Mathematics, 73(1) (2018), Article 9.
  • [16] 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.
  • [17] Kim YK., Ghil BM., Integrals of fuzzy-number-valued functions, Fuzzy Sets Syst. 86 (1997), 213-222.
  • [18] Matloka M., Sequences of fuzzy numbers, Busefal, 28 (1986), 28-37.
  • [19] Nanda S., On sequences of fuzzy numbers, Fuzzy Sets Systems, 33 (1989), 123-126.
  • [20] Mohiuddine SA, Alamri BAS., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matem´aticas RACSAM 113(3) (2019), 1955-1973.
  • [21] Mohiuddine SA., Asiri A., Hazarika B., Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst. 48(5) (2019), 492-506.
  • [22] Mohiuddine S.A. Statistical weighted A-summability with application to Korovkin’s type approximation theorem, J. Inequal. Appl. 2016(101) (2016), https://doi.org/10.1186/s13660-016-1040-1
  • [23] Negoita CV., Ralescu D., Applications of fuzzy sets to systems analysis, (1975), Wiley, New York
  • [24] Nuray F, Savaş E., Statistical convergence of sequences of fuzzy numbers, Math Slovaca, 45(3) (1995), 269-273.
  • [25] Nuray F., Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets and Systems, 99 (1998) 353-355.
  • [26] Salat T., On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.
  • [27] Savas¸ E., On statistically convergent sequences of fuzzy numbers, Inform. Sci. 137(1-4) (2001), 277-282.
  • [28] Schoenberg IJ., The integrability of certain functions and related summability methods, Am. Math. Monthly, 66 (1959), 361-375.
  • [29] Şençimen, C., Pehlivan, S., Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems, 159 (2008), 361-370.
  • [30] Türkmen M.R., Çınar M., Lacunary-statistical convergence in fuzzy normed linear spaces, Appl. Comp. Math. 6(5) (2017), 233-237.
  • [31] Türkmen M.R., Dündar E., On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces, J. Intel. Fuzzy Syst. 36(2) (2019), 1683-1690.
  • [32] Ulusu U., Nuray F., Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics, 4(2) (2012), 99-109.
  • [33] Ulusu U., Dündar E., I-lacunary statistical convergence of sequences of sets, Filomat, 28(8) (2014), 1567-1574.
  • [34] Ulusu U., Nuray F., Lacunary statistical summability of sequences of sets, Konuralp Journal of Mathematics, 3(2) (2015), 176-184.
  • [35] Zadeh L.A., Fuzzy sets, Inform. Control, 8 (1965), 338-353.
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ömer Kişi 0000-0003-3264-6239

Erdinç Dündar 0000-0002-0545-7486

Yayımlanma Tarihi 27 Ekim 2020
Gönderilme Tarihi 14 Mayıs 2020
Kabul Tarihi 13 Temmuz 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 2

Kaynak Göster

APA Kişi, Ö., & Dündar, E. (2020). Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions. Konuralp Journal of Mathematics, 8(2), 252-262.
AMA Kişi Ö, Dündar E. Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions. Konuralp J. Math. Ekim 2020;8(2):252-262.
Chicago Kişi, Ömer, ve Erdinç Dündar. “Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions”. Konuralp Journal of Mathematics 8, sy. 2 (Ekim 2020): 252-62.
EndNote Kişi Ö, Dündar E (01 Ekim 2020) Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions. Konuralp Journal of Mathematics 8 2 252–262.
IEEE Ö. Kişi ve E. Dündar, “Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions”, Konuralp J. Math., c. 8, sy. 2, ss. 252–262, 2020.
ISNAD Kişi, Ömer - Dündar, Erdinç. “Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions”. Konuralp Journal of Mathematics 8/2 (Ekim 2020), 252-262.
JAMA Kişi Ö, Dündar E. Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions. Konuralp J. Math. 2020;8:252–262.
MLA Kişi, Ömer ve Erdinç Dündar. “Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions”. Konuralp Journal of Mathematics, c. 8, sy. 2, 2020, ss. 252-6.
Vancouver Kişi Ö, Dündar E. Lacunary Statistical Convergence in Measure for Sequences of Fuzzy Valued Functions. Konuralp J. Math. 2020;8(2):252-6.
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