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A-statistically localized sequences in n-normed spaces

Yıl 2020, Cilt: 69 Sayı: 2, 1484 - 1497, 31.12.2020

Mehmet Gürdal Nur Sarı Ekrem Savaş

https://doi.org/10.31801/cfsuasmas.704446
Cited By: 3

Öz

In 1974, Krivonosov defined the concept of localized sequence that is defined as a generalization of Cauchy sequence in metric spaces. In this present work, the A-statistically localized sequences in n-normed spaces are defined and some main properties of A-statistically localized sequences are given. Also, it is shown that a sequence is A-statistically Cauchy iff its A-statistical barrier is equal to zero. Moreover, we define the uniformly A-statistically localized sequences on n-normed spaces and investigate its relationship with A-statistically Cauchy sequences.

Anahtar Kelimeler

A-statistical convergence n-normed spaces A-statistical localor of the sequence

Kaynakça

  • Connor, B. J., The statistical and strong p-Cesaro convergence of sequences, Analysis (Munich), 8 (1988), 47-63.
  • Connor, J. , Kline, J., On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl., 197 (1996), 392-399.
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • Fridy, J. A., On statistical convergence, Analysis (Munich), 5 (1985), 301-313.
  • Gähler, S., 2-metrische Räume und ihre topologische Struktur, Math. Nachr., 26 (1963), 115-148.
  • Gähler, S., Lineare 2-normierte räume, Math. Nachr., 28(1-2) (1964), 1-43.
  • Gähler, S., Untersuchungen über verallgemeinerte m-metrische räume. I., Math. Nachr., 40(1-3) (1969), 165-189
  • Gähler, S., Siddiqi, A. H., Gupta, S.C., Contributions to non-archimedean functional analysis, Math. Nachr., 69 (1963), 162-171.
  • Gunawan, H., Mashadi, On n-normed Spaces, Int. J. Math. Sci., 27(10) (2001), 631-639.
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-Banach spaces, Thai. J. Math., 2(1) (2004), 107-113.
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-normed spaces, Southeast Asian Bull. Math., 33(2) (2009), 257-264.
  • Gürdal, M., Açık, I., On I-cauchy sequences in 2-normed spaces, Math. Inequal. Appl., 11(2) (2008), 349-354.
  • Gürdal, M., Şahiner, A., Statistical approximation with a sequence of 2-Banach spaces, Math. Comput. Modelling, 55(3-4) (2012), 471-479.
  • Gürdal, M., Şahiner, A., Açık, I., Approximation theory in 2-Banach spaces, Nonlinear Anal., 71(5-6) (2009), 1654-1661.
  • Gürdal, M., Yamancı, U., Statistical convergence and some questions of operator theory, Dynam. Syst. Appl., 24 (2015), 305-312.
  • 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 Math., (2018), 73:9.
  • Kolk, E., The statistical convergence in Banach spaces, Acta et Commentationes Universitatis Tartuensis, 928 (1991), 41-52.
  • Krivonosov, L. N., Localized sequences in metric spaces, Izv. Vyssh. Uchebn. Zaved. Mat., 4 (1974), 45-54; Soviet Math. (Iz. VUZ), 18(4), 37-44.
  • Mohiuddine, S. A., Statistical weighted A-summability with application to Korovkin's type approximation theorem, J. Inequal. Appl., (2016), 2016:101.
  • Mohiuddine, S. A., Alamri, B. A. S., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 113 (2019), 1955-1973.
  • 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. Gen. Syst., 48(5) (2019), 492-506. Mohiuddine, S. A., Hazarika, B., Alghamdi, M. A., Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33(14) (2019), 4549-4560.
  • Mohiuddine, S. A., Şevli, H., Cancan, M., Statistical convergence in fuzzy 2-normed space, J. Comput. Anal. Appl., 12(4) (2010), 787-798. Mursaleen, M., On statistical convergence in random 2-normed spaces, Acta Sci. Math. (Szeged), 76 (2010), 101-109.
  • Nabiev, A. A., Savaş, E., Gürdal, M., Statistically localized sequences in metric spaces. J. App. Anal. Comp., 9(2) (2019), 739-746. Nabiev, A. A., Savaş, E., Gürdal, M., I-localized sequences in metric spaces, Facta Univ. Ser. Math. Inform., 35(2) (2020), 459-469.
  • Rath, D., Tripathy, B.C., On statistically convergent and statistically Cauchy sequences, Indian J. Pure Appl. Math., 25(4) (1994), 381-386.
  • Raymond, W. F., Cho, Ye. J., Geometry of linear 2-normed spaces, Huntington, N.Y. Nova Science Publishers, 2001.
  • Šalát, T., On statistically convergent sequences of real numbers, Mathematica Slovaca, 30(2) (1980), 139-150.
  • Savaş, E., A-statistical convergence of order α via ϕ-function, Appl. Anal. Discrete Math., 13 (2019), 918-926.
  • Savaş E. and Gürdal M., Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Syst., 27(4) (2014), 1621-1629.
  • Savaş E., Gürdal M., Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Syst., 27(4) (2014), 2067-2075.
  • Savaş, E., Gürdal, M., Ideal convergent function sequences in random 2-normed spaces, Filomat, 30(3) (2016), 557-567.
  • Savaş, E., Yamancı, U., Gürdal, M., I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019), 2324-2332.
  • Savaş, R., λ-double statistical convergence of functions, Filomat, 33(2) (2019), 519-524.
  • Savaş, R., Öztürk, M., On generalized ideal asymptotically statistical equivalent of order α for functions, Ukr. Math. J., 70 (2019), 1901-1912.
  • Savaş, R.,, Sezer, S. A., Tauberian theorems for sequences in 2-normed spaces, Results Math., 72 (2017), 1919-1931.
  • Savaş, R. , Patterson, R. F., I₂-lacunary strongly summability for multidimensional measurable functions, Pub. I. Math-Beograd, 107(121) (2020), 93-107.
  • Şahiner, A., Gürdal, M., Yiğit, T., Ideal convergence characterization of the completion of linear n-normed spaces, Comput. Math. Appl., 61(3) (2011), 683-689.
  • Siddiqi, A. H., 2-normed spaces, Aligarh Bull. Math., (1980), 53-70.
  • Vulich, B., On a generalized notion of convergence in a Banach space, Ann. Math., 38(1) (1937), 156-174.
  • Yamancı, U., Gürdal, M., Statistical convergence and operators on Fock space, New York J. Math., 22 (2016), 199-207.
  • Yamancı, U., Nabiev, A. A., Gürdal, M., Statistically localized sequences in 2-normed spaces, Honam Math. J., 42(1) (2020), 161-173. Yamancı, U., Savaş, E., Gürdal, M., I-localized sequences in two normed spaces, Malays. J. Math. Sci., 14(3) (2020), 491-503.
  • Yegül, S., Dündar, E., On statistical convergence of sequences of functions in 2-normed spaces, J. Classical Anal., 10(1) (2017), 49-57.
  • Yegül, S., Dündar, E., Statistical convergence of double sequences of functions and some properties in 2-normed spaces, Facta Univ. Ser. Math. Inform., 33(5) (2018), 705-719.

Yıl 2020, Cilt: 69 Sayı: 2, 1484 - 1497, 31.12.2020

Mehmet Gürdal Nur Sarı Ekrem Savaş

https://doi.org/10.31801/cfsuasmas.704446
Cited By: 3

Öz

Kaynakça

  • Connor, B. J., The statistical and strong p-Cesaro convergence of sequences, Analysis (Munich), 8 (1988), 47-63.
  • Connor, J. , Kline, J., On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl., 197 (1996), 392-399.
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • Fridy, J. A., On statistical convergence, Analysis (Munich), 5 (1985), 301-313.
  • Gähler, S., 2-metrische Räume und ihre topologische Struktur, Math. Nachr., 26 (1963), 115-148.
  • Gähler, S., Lineare 2-normierte räume, Math. Nachr., 28(1-2) (1964), 1-43.
  • Gähler, S., Untersuchungen über verallgemeinerte m-metrische räume. I., Math. Nachr., 40(1-3) (1969), 165-189
  • Gähler, S., Siddiqi, A. H., Gupta, S.C., Contributions to non-archimedean functional analysis, Math. Nachr., 69 (1963), 162-171.
  • Gunawan, H., Mashadi, On n-normed Spaces, Int. J. Math. Sci., 27(10) (2001), 631-639.
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-Banach spaces, Thai. J. Math., 2(1) (2004), 107-113.
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-normed spaces, Southeast Asian Bull. Math., 33(2) (2009), 257-264.
  • Gürdal, M., Açık, I., On I-cauchy sequences in 2-normed spaces, Math. Inequal. Appl., 11(2) (2008), 349-354.
  • Gürdal, M., Şahiner, A., Statistical approximation with a sequence of 2-Banach spaces, Math. Comput. Modelling, 55(3-4) (2012), 471-479.
  • Gürdal, M., Şahiner, A., Açık, I., Approximation theory in 2-Banach spaces, Nonlinear Anal., 71(5-6) (2009), 1654-1661.
  • Gürdal, M., Yamancı, U., Statistical convergence and some questions of operator theory, Dynam. Syst. Appl., 24 (2015), 305-312.
  • 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 Math., (2018), 73:9.
  • Kolk, E., The statistical convergence in Banach spaces, Acta et Commentationes Universitatis Tartuensis, 928 (1991), 41-52.
  • Krivonosov, L. N., Localized sequences in metric spaces, Izv. Vyssh. Uchebn. Zaved. Mat., 4 (1974), 45-54; Soviet Math. (Iz. VUZ), 18(4), 37-44.
  • Mohiuddine, S. A., Statistical weighted A-summability with application to Korovkin's type approximation theorem, J. Inequal. Appl., (2016), 2016:101.
  • Mohiuddine, S. A., Alamri, B. A. S., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 113 (2019), 1955-1973.
  • 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. Gen. Syst., 48(5) (2019), 492-506. Mohiuddine, S. A., Hazarika, B., Alghamdi, M. A., Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33(14) (2019), 4549-4560.
  • Mohiuddine, S. A., Şevli, H., Cancan, M., Statistical convergence in fuzzy 2-normed space, J. Comput. Anal. Appl., 12(4) (2010), 787-798. Mursaleen, M., On statistical convergence in random 2-normed spaces, Acta Sci. Math. (Szeged), 76 (2010), 101-109.
  • Nabiev, A. A., Savaş, E., Gürdal, M., Statistically localized sequences in metric spaces. J. App. Anal. Comp., 9(2) (2019), 739-746. Nabiev, A. A., Savaş, E., Gürdal, M., I-localized sequences in metric spaces, Facta Univ. Ser. Math. Inform., 35(2) (2020), 459-469.
  • Rath, D., Tripathy, B.C., On statistically convergent and statistically Cauchy sequences, Indian J. Pure Appl. Math., 25(4) (1994), 381-386.
  • Raymond, W. F., Cho, Ye. J., Geometry of linear 2-normed spaces, Huntington, N.Y. Nova Science Publishers, 2001.
  • Šalát, T., On statistically convergent sequences of real numbers, Mathematica Slovaca, 30(2) (1980), 139-150.
  • Savaş, E., A-statistical convergence of order α via ϕ-function, Appl. Anal. Discrete Math., 13 (2019), 918-926.
  • Savaş E. and Gürdal M., Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Syst., 27(4) (2014), 1621-1629.
  • Savaş E., Gürdal M., Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces, J. Intell. Fuzzy Syst., 27(4) (2014), 2067-2075.
  • Savaş, E., Gürdal, M., Ideal convergent function sequences in random 2-normed spaces, Filomat, 30(3) (2016), 557-567.
  • Savaş, E., Yamancı, U., Gürdal, M., I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019), 2324-2332.
  • Savaş, R., λ-double statistical convergence of functions, Filomat, 33(2) (2019), 519-524.
  • Savaş, R., Öztürk, M., On generalized ideal asymptotically statistical equivalent of order α for functions, Ukr. Math. J., 70 (2019), 1901-1912.
  • Savaş, R.,, Sezer, S. A., Tauberian theorems for sequences in 2-normed spaces, Results Math., 72 (2017), 1919-1931.
  • Savaş, R. , Patterson, R. F., I₂-lacunary strongly summability for multidimensional measurable functions, Pub. I. Math-Beograd, 107(121) (2020), 93-107.
  • Şahiner, A., Gürdal, M., Yiğit, T., Ideal convergence characterization of the completion of linear n-normed spaces, Comput. Math. Appl., 61(3) (2011), 683-689.
  • Siddiqi, A. H., 2-normed spaces, Aligarh Bull. Math., (1980), 53-70.
  • Vulich, B., On a generalized notion of convergence in a Banach space, Ann. Math., 38(1) (1937), 156-174.
  • Yamancı, U., Gürdal, M., Statistical convergence and operators on Fock space, New York J. Math., 22 (2016), 199-207.
  • Yamancı, U., Nabiev, A. A., Gürdal, M., Statistically localized sequences in 2-normed spaces, Honam Math. J., 42(1) (2020), 161-173. Yamancı, U., Savaş, E., Gürdal, M., I-localized sequences in two normed spaces, Malays. J. Math. Sci., 14(3) (2020), 491-503.
  • Yegül, S., Dündar, E., On statistical convergence of sequences of functions in 2-normed spaces, J. Classical Anal., 10(1) (2017), 49-57.
  • Yegül, S., Dündar, E., Statistical convergence of double sequences of functions and some properties in 2-normed spaces, Facta Univ. Ser. Math. Inform., 33(5) (2018), 705-719.
Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Mehmet Gürdal 0000-0003-0866-1869

Nur Sarı Bu kişi benim 0000-0002-3639-975X

Ekrem Savaş 0000-0003-2135-3094

Yayımlanma Tarihi 31 Aralık 2020
Gönderilme Tarihi 16 Mart 2020
Kabul Tarihi 2 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 2

Kaynak Göster

APA Gürdal, M., Sarı, N., & Savaş, E. (2020). A-statistically localized sequences in n-normed spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1484-1497. https://doi.org/10.31801/cfsuasmas.704446
AMA Gürdal M, Sarı N, Savaş E. A-statistically localized sequences in n-normed spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2020;69(2):1484-1497. doi:10.31801/cfsuasmas.704446
Chicago Gürdal, Mehmet, Nur Sarı, ve Ekrem Savaş. “A-Statistically Localized Sequences in N-Normed Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 2 (Aralık 2020): 1484-97. https://doi.org/10.31801/cfsuasmas.704446.
EndNote Gürdal M, Sarı N, Savaş E (01 Aralık 2020) A-statistically localized sequences in n-normed spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1484–1497.
IEEE M. Gürdal, N. Sarı, ve E. Savaş, “A-statistically localized sequences in n-normed spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 2, ss. 1484–1497, 2020, doi: 10.31801/cfsuasmas.704446.
ISNAD Gürdal, Mehmet vd. “A-Statistically Localized Sequences in N-Normed Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (Aralık 2020), 1484-1497. https://doi.org/10.31801/cfsuasmas.704446.
JAMA Gürdal M, Sarı N, Savaş E. A-statistically localized sequences in n-normed spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1484–1497.
MLA Gürdal, Mehmet vd. “A-Statistically Localized Sequences in N-Normed Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 2, 2020, ss. 1484-97, doi:10.31801/cfsuasmas.704446.
Vancouver Gürdal M, Sarı N, Savaş E. A-statistically localized sequences in n-normed spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1484-97.

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