Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2022, Cilt: 5 Sayı: 1, 1 - 10, 15.02.2023

Ahmet Sahiner , Nurullah Yılmaz

Öz

Kaynakça

  • M. Asadi, B. E. Rhoades and H. Soleimani, Some notes on the paper ``The equivalance of cone metric space and metric space'', Fixed Point Theory and A. 87 2012, 1-4.
  • J. Connor, $R-$ type summability methods, Cauchy criteria, $P-$ sets and statistical convergence, Proc. Am. Math. Soc. 115(2) 1992, 319-327.
  • J. Connor, Two valued measure and summability, Analysis. 10 1992, 373-385.
  • P. Das and S. Bhunia, Two valued measure and summability of double sequences, Czechoslovak Math. J. 59(134) 2009, 1141-1155.
  • P. Das, E. Savas and S. Bhunia, Two valued measure and some new double sequence spaces in 2-normed spaces, Czechoslovak Math. J., 61(136) 2011, 809-825.
  • P. Das and S. Bhunia, Two valued measure and summability of double sequences in asymmetric context, Acta Math. Hungar., 130(1-2) (2011), 167-187.
  • W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. TMA 72 2010, 2259-2261.
  • H. Fast, Sur la convergence statistique. Colloq. Math. 2 1951, 241-244.
  • Y. Feng and W. Mao, The equivalence of cone metric spaces and metric spaces, Fixed Point Theory. 11(2) 2010, 259-264.
  • M. Frechet, La notion decart et le calcul fonctionnel, C.R. Math. Acad. Sci. Paris, 140 1905, 772-774.
  • M. Frechet, Sur quelques point du calcul fonctionnel, Rend. Circ. Mat. Palermo, 22 1906, 1-74.
  • J. A. Fridy, On statistical convergence, Analysis 5 1985, 301-313.
  • S. Jankovic, Z. Kadelburg and S. Radenovic, On cone metric spaces: A survey, Nonlinear Anal. 74 2011, 2591-2601.
  • Z. Kadelburg, S. Radenovic and V. Rakocevic, A note on the equivalence of some metric and cone metric fixed point results, Appl. Math. Lett. 24 2011, 370-374.
  • H. Long-Guang and Z. Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 2007, 1468-1476.
  • N. Malviya and S. Chouhan, Proving fixed point theorems using general principles in cone Banach spaces, Int. Math. Forum 6(3) 2011, 115-123.
  • M. Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl.,288 2003, 223-231.
  • F. Moricz, Statistical convergence of multiple sequences, Arc. Math. 81 2003, 82-89.
  • Sh. Rezapour and R. Halmbarani, Some notes on the paper ``Cone metric spaces and fixed point theorems of contractive mappings'', J. Math. Anal. Appl., 345 2008, 719-724.
  • A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann. 53 1900, 289-321.
  • A. Proinov, A unified theory of cone metric spaces and its applications to the fixed point theory, Fixed Point Theory A., 103 2013, 1-38.
  • A. Sahiner, Fixed point theorems in symmetric $2-$cone Banach space $\left(l_p,\Vert \cdot,\cdot\Vert_{p}^{c}\right)$, Journal of Nonlinear Analysis and Optimization. 3(2) 2012, 115-120.
  • A. Sahiner and N. Yilmaz, Multiple sequences in cone metric spaces, Journal of Applied and Engineering Mathematics, 4(2) 2014, 226-233.
  • T. \v{S}al\'{a}t, On statistically convergent sequences of real numbers, Math. Slovaca, 30 1980, 139-150.
  • W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results. Comput.Math. Appl. 60 2010, 2508-2515.
  • W. Shatanawi, V. C. Rajic, S. Radenovic and A. Al-Rawashdeh, Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces. Fixed Point Theory A., 106 2012, 1-7.
  • I.J. Schoenberg, The integrability of certain functions and related summability methods. Amer. Math. Mothly 66 1959, 361-375.
  • P. P. Zabrejko, $K-$metric and $K-$ normed linear spaces: survey, Collect. Math., 48 1997, 825-859.
  • E. Savas, On two-valued measure and double statistical convergence in $2-$normed spaces, J. Ineq. Appl. 347 2013, 1-11.
  • B. T. Bilalov and S. R. Sadigova, On $\mu-$statistical convergence, Proc. Amer. Math. Soc. 143(9) 2015, 3869-–3878.
  • R. Haloi and M. Sen, $\mu-$statistically convergent multiple sequences in probabilistic normed spaces, Advances in Algebra and Analysis, Springer, (2018) 353-360.
  • A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Selçuk J. Appl. Math., 8(2) 2007, 49 - 55.
  • K. Li, S. Lin and Y. Ge, On statistical convergence in cone metric spaces, Topology and its Applications 196 2015, 641–-651.
  • S. Aleksić, Z. Kadelburg, Z. D. Mitrovic and S. Radenovic, A new survey: cone metric spaces. J. Int. Math. Virtual Inst. 9 2019, 93-–121.

$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES

Yıl 2022, Cilt: 5 Sayı: 1, 1 - 10, 15.02.2023

Ahmet Sahiner , Nurullah Yılmaz

Öz

The concept of $\mu$-statistical convergence of double and
multiple sequences in topological vector space (tvs for short) valued
cone metric spaces is introduced in this paper. The relationships
between $\mu$-statistical convergence and convergence in $\mu$-density is
investigated.

Anahtar Kelimeler

cone metric multiple sequence two valued measure statistical convergence.

Kaynakça

  • M. Asadi, B. E. Rhoades and H. Soleimani, Some notes on the paper ``The equivalance of cone metric space and metric space'', Fixed Point Theory and A. 87 2012, 1-4.
  • J. Connor, $R-$ type summability methods, Cauchy criteria, $P-$ sets and statistical convergence, Proc. Am. Math. Soc. 115(2) 1992, 319-327.
  • J. Connor, Two valued measure and summability, Analysis. 10 1992, 373-385.
  • P. Das and S. Bhunia, Two valued measure and summability of double sequences, Czechoslovak Math. J. 59(134) 2009, 1141-1155.
  • P. Das, E. Savas and S. Bhunia, Two valued measure and some new double sequence spaces in 2-normed spaces, Czechoslovak Math. J., 61(136) 2011, 809-825.
  • P. Das and S. Bhunia, Two valued measure and summability of double sequences in asymmetric context, Acta Math. Hungar., 130(1-2) (2011), 167-187.
  • W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. TMA 72 2010, 2259-2261.
  • H. Fast, Sur la convergence statistique. Colloq. Math. 2 1951, 241-244.
  • Y. Feng and W. Mao, The equivalence of cone metric spaces and metric spaces, Fixed Point Theory. 11(2) 2010, 259-264.
  • M. Frechet, La notion decart et le calcul fonctionnel, C.R. Math. Acad. Sci. Paris, 140 1905, 772-774.
  • M. Frechet, Sur quelques point du calcul fonctionnel, Rend. Circ. Mat. Palermo, 22 1906, 1-74.
  • J. A. Fridy, On statistical convergence, Analysis 5 1985, 301-313.
  • S. Jankovic, Z. Kadelburg and S. Radenovic, On cone metric spaces: A survey, Nonlinear Anal. 74 2011, 2591-2601.
  • Z. Kadelburg, S. Radenovic and V. Rakocevic, A note on the equivalence of some metric and cone metric fixed point results, Appl. Math. Lett. 24 2011, 370-374.
  • H. Long-Guang and Z. Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 2007, 1468-1476.
  • N. Malviya and S. Chouhan, Proving fixed point theorems using general principles in cone Banach spaces, Int. Math. Forum 6(3) 2011, 115-123.
  • M. Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl.,288 2003, 223-231.
  • F. Moricz, Statistical convergence of multiple sequences, Arc. Math. 81 2003, 82-89.
  • Sh. Rezapour and R. Halmbarani, Some notes on the paper ``Cone metric spaces and fixed point theorems of contractive mappings'', J. Math. Anal. Appl., 345 2008, 719-724.
  • A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann. 53 1900, 289-321.
  • A. Proinov, A unified theory of cone metric spaces and its applications to the fixed point theory, Fixed Point Theory A., 103 2013, 1-38.
  • A. Sahiner, Fixed point theorems in symmetric $2-$cone Banach space $\left(l_p,\Vert \cdot,\cdot\Vert_{p}^{c}\right)$, Journal of Nonlinear Analysis and Optimization. 3(2) 2012, 115-120.
  • A. Sahiner and N. Yilmaz, Multiple sequences in cone metric spaces, Journal of Applied and Engineering Mathematics, 4(2) 2014, 226-233.
  • T. \v{S}al\'{a}t, On statistically convergent sequences of real numbers, Math. Slovaca, 30 1980, 139-150.
  • W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results. Comput.Math. Appl. 60 2010, 2508-2515.
  • W. Shatanawi, V. C. Rajic, S. Radenovic and A. Al-Rawashdeh, Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces. Fixed Point Theory A., 106 2012, 1-7.
  • I.J. Schoenberg, The integrability of certain functions and related summability methods. Amer. Math. Mothly 66 1959, 361-375.
  • P. P. Zabrejko, $K-$metric and $K-$ normed linear spaces: survey, Collect. Math., 48 1997, 825-859.
  • E. Savas, On two-valued measure and double statistical convergence in $2-$normed spaces, J. Ineq. Appl. 347 2013, 1-11.
  • B. T. Bilalov and S. R. Sadigova, On $\mu-$statistical convergence, Proc. Amer. Math. Soc. 143(9) 2015, 3869-–3878.
  • R. Haloi and M. Sen, $\mu-$statistically convergent multiple sequences in probabilistic normed spaces, Advances in Algebra and Analysis, Springer, (2018) 353-360.
  • A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Selçuk J. Appl. Math., 8(2) 2007, 49 - 55.
  • K. Li, S. Lin and Y. Ge, On statistical convergence in cone metric spaces, Topology and its Applications 196 2015, 641–-651.
  • S. Aleksić, Z. Kadelburg, Z. D. Mitrovic and S. Radenovic, A new survey: cone metric spaces. J. Int. Math. Virtual Inst. 9 2019, 93-–121.
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ahmet Sahiner

Nurullah Yılmaz

Yayımlanma Tarihi 15 Şubat 2023
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 1

Kaynak Göster

APA Sahiner, A., & Yılmaz, N. (2023). $\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES. Journal of Multidisciplinary Modeling and Optimization, 5(1), 1-10.
AMA Sahiner A, Yılmaz N. $\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES. jmmo. Şubat 2023;5(1):1-10.
Chicago Sahiner, Ahmet, ve Nurullah Yılmaz. “$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES”. Journal of Multidisciplinary Modeling and Optimization 5, sy. 1 (Şubat 2023): 1-10.
EndNote Sahiner A, Yılmaz N (01 Şubat 2023) $\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES. Journal of Multidisciplinary Modeling and Optimization 5 1 1–10.
IEEE A. Sahiner ve N. Yılmaz, “$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES”, jmmo, c. 5, sy. 1, ss. 1–10, 2023.
ISNAD Sahiner, Ahmet - Yılmaz, Nurullah. “$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES”. Journal of Multidisciplinary Modeling and Optimization 5/1 (Şubat 2023), 1-10.
JAMA Sahiner A, Yılmaz N. $\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES. jmmo. 2023;5:1–10.
MLA Sahiner, Ahmet ve Nurullah Yılmaz. “$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES”. Journal of Multidisciplinary Modeling and Optimization, c. 5, sy. 1, 2023, ss. 1-10.
Vancouver Sahiner A, Yılmaz N. $\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES. jmmo. 2023;5(1):1-10.
 Kapak Resmi İndir