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MULTIPLE SEQUENCES IN CONE METRIC SPACES

Yıl 2014, Cilt: 4 Sayı: 2, 226 - 233, 01.12.2014

Öz

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.

Kaynakça

  • 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.
Yıl 2014, Cilt: 4 Sayı: 2, 226 - 233, 01.12.2014

Öz

Kaynakça

  • 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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

A. Sahiner Bu kişi benim

N. Yılmaz Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 4 Sayı: 2

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