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MULTIPLE SEQUENCES IN CONE METRIC SPACES

Year 2014, Volume: 4 Issue: 2, 226 - 233, 01.12.2014

Abstract

In this study, we introduce the ordinary and statistical convergence of double and multiple sequences in cone metric spaces. Moreover, the relationships between these convergence types are also invastigated.

References

  • Long-Guang, H., Xian, Z., (2007), Cone metric spaces and fixed point theorems of contractive map- pings, J. Math. Anal. Appl., 332 , 1468–1476.
  • Jankovic, S., Kadelburg, Z., (2011), Radenovic, S., On cone metric spaces: A survey, Nonlinear Anal. 2591-2601.
  • Shatanawi, W., (2010), Partially ordered cone metric spaces and coupled fixed point results, Com- put.Math. Appl. 60 2508-2515.
  • Feng, Y., Mao, W., (2010), The equivalence of cone metric spaces and metric spaces, Fixed Point Theory 11, no. 2, 259-264.
  • Malviya, N., Chouhan, S., (2011), Proving fixed point theorems using general principles in cone
  • Banach spaces, Int. Math. Forum 6 no.3, 115-123. Rezapour, Sh., Halmbarani, R., (2008), Some notes on the paper “Cone metric spaces andfixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345, 719–724.
  • Sahiner, A., (2012), Fixed Point Theorems in Symmetric 2− Cone Banach Spacelp,∥·, ·∥p, Journal ( ) of Nonlinear Analysis and Optimization, 3 no. 2, 115–120.
  • Du, W. S., (2010), A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. TMA, 72, 2259-2261.
  • Kadelburg, Z., Radenovic, S., Rakocevic, V., (2011), A note on the equivalence of some metric and cone metric fixed point results, Appl. Math. Lett. 24, 370–374.
  • Proinov, P., (2013), A unified theory of cone metric spaces and its applications to the fixed point theory, Fixed Point Theory A, 103.
  • Das, P., Bhunia, S., (2009), Two valued measure and summability of double sequences, Czechoslovak Math. J., 59, no. 134, 1141–1155.
  • Das, P. Bhunia, S., (2011), Two valued measure and summability of double sequences in asymmetric context, Acta Math. Hungar., 130 no. 1-2, 167–187.
  • Fast, H., (1951), Sur la convergence statistique, Colloq. Math., 2, 241–244.
  • Schoenberg, I. J., (1959), The integrability of certain functions and related summability methods, Amer. Math. Mothly 66 361–375. ˇSal´at, T., (1980), On statistically convergent sequences of real numbers, Math. Slovaca 30, 139–150.
  • Fridy, J. A., (1985), On statistical convergence, Analysis 5 301–313.
  • Connor, J., (1992), R− type summability methods, Cauchy criteria, P − sets and statistical conver- gence, Proc. Amer. Math. Soc., 115(1992), 319–327.
  • Tas, E., Yurdakadim, T., (2012), Characterization of uniform statistical convergence for double se- quences, Miskolc Math. Notes, 13 no. 2, 2543–553.
  • Das, P., Savas, E., Bhunia, S., (2011), Two valued measure and some new double sequence spaces in normed spaces, Czechoslovak Math. J., 61, no. 136, 809–825.
  • Mursaleen, M., Edely, O. H. H., (2003), Statistical convergence of double sequences, J. Math. Anal. Appl., 288, 223–231.
  • Moricz, F.,(2003) Statistical convergence of multiple sequences, Arc. Math. 81, 82–89.
  • Pringsheim, A., (1900) Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53, 289–321.
Year 2014, Volume: 4 Issue: 2, 226 - 233, 01.12.2014

Abstract

References

  • Long-Guang, H., Xian, Z., (2007), Cone metric spaces and fixed point theorems of contractive map- pings, J. Math. Anal. Appl., 332 , 1468–1476.
  • Jankovic, S., Kadelburg, Z., (2011), Radenovic, S., On cone metric spaces: A survey, Nonlinear Anal. 2591-2601.
  • Shatanawi, W., (2010), Partially ordered cone metric spaces and coupled fixed point results, Com- put.Math. Appl. 60 2508-2515.
  • Feng, Y., Mao, W., (2010), The equivalence of cone metric spaces and metric spaces, Fixed Point Theory 11, no. 2, 259-264.
  • Malviya, N., Chouhan, S., (2011), Proving fixed point theorems using general principles in cone
  • Banach spaces, Int. Math. Forum 6 no.3, 115-123. Rezapour, Sh., Halmbarani, R., (2008), Some notes on the paper “Cone metric spaces andfixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345, 719–724.
  • Sahiner, A., (2012), Fixed Point Theorems in Symmetric 2− Cone Banach Spacelp,∥·, ·∥p, Journal ( ) of Nonlinear Analysis and Optimization, 3 no. 2, 115–120.
  • Du, W. S., (2010), A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. TMA, 72, 2259-2261.
  • Kadelburg, Z., Radenovic, S., Rakocevic, V., (2011), A note on the equivalence of some metric and cone metric fixed point results, Appl. Math. Lett. 24, 370–374.
  • Proinov, P., (2013), A unified theory of cone metric spaces and its applications to the fixed point theory, Fixed Point Theory A, 103.
  • Das, P., Bhunia, S., (2009), Two valued measure and summability of double sequences, Czechoslovak Math. J., 59, no. 134, 1141–1155.
  • Das, P. Bhunia, S., (2011), Two valued measure and summability of double sequences in asymmetric context, Acta Math. Hungar., 130 no. 1-2, 167–187.
  • Fast, H., (1951), Sur la convergence statistique, Colloq. Math., 2, 241–244.
  • Schoenberg, I. J., (1959), The integrability of certain functions and related summability methods, Amer. Math. Mothly 66 361–375. ˇSal´at, T., (1980), On statistically convergent sequences of real numbers, Math. Slovaca 30, 139–150.
  • Fridy, J. A., (1985), On statistical convergence, Analysis 5 301–313.
  • Connor, J., (1992), R− type summability methods, Cauchy criteria, P − sets and statistical conver- gence, Proc. Amer. Math. Soc., 115(1992), 319–327.
  • Tas, E., Yurdakadim, T., (2012), Characterization of uniform statistical convergence for double se- quences, Miskolc Math. Notes, 13 no. 2, 2543–553.
  • Das, P., Savas, E., Bhunia, S., (2011), Two valued measure and some new double sequence spaces in normed spaces, Czechoslovak Math. J., 61, no. 136, 809–825.
  • Mursaleen, M., Edely, O. H. H., (2003), Statistical convergence of double sequences, J. Math. Anal. Appl., 288, 223–231.
  • Moricz, F.,(2003) Statistical convergence of multiple sequences, Arc. Math. 81, 82–89.
  • Pringsheim, A., (1900) Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53, 289–321.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

A. Sahiner This is me

N. Yılmaz This is me

Publication Date December 1, 2014
Published in Issue Year 2014 Volume: 4 Issue: 2

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