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Year 2022, Volume: 5 Issue: 1, 1 - 10, 15.02.2023

Ahmet Sahiner , Nurullah Yılmaz

Abstract

References

  • 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

Year 2022, Volume: 5 Issue: 1, 1 - 10, 15.02.2023

Ahmet Sahiner , Nurullah Yılmaz

Abstract

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.

Keywords

cone metric multiple sequence two valued measure statistical convergence.

References

  • 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.
There are 34 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ahmet Sahiner

Nurullah Yılmaz

Publication Date February 15, 2023
Published in Issue Year 2022 Volume: 5 Issue: 1

Cite

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. February 2023;5(1):1-10.
Chicago Sahiner, Ahmet, and Nurullah Yılmaz. “$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES”. Journal of Multidisciplinary Modeling and Optimization 5, no. 1 (February 2023): 1-10.
EndNote Sahiner A, Yılmaz N (February 1, 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 and N. Yılmaz, “$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES”, jmmo, vol. 5, no. 1, pp. 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 (February 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 and Nurullah Yılmaz. “$\mu$-STATISTICAL CONVERGENCE OF MULTIPLE SEQUENCES IN TOPOLOGICAL VECTOR VALUED CONE METRIC SPACES”. Journal of Multidisciplinary Modeling and Optimization, vol. 5, no. 1, 2023, pp. 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.
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