On certain new notion of order Cauchy sequences, continuity in (l)-group

• Pal, Sudip Kumar ^[2] ; Chakraborty, Sagar ^[1]
  1. [1] Jadavpur University

     Jadavpur University

     India

     
  2. [2] Diamond Harbour Women's University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 1, 2022, págs. 55-68
• Idioma: inglés
• DOI: 10.4995/agt.2022.16126
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce the notion order quasi-Cauchy se-quences, downward and upward order quasi-cauchy sequences, order half Cauchy sequences. Next we consider associated idea of continuity namely, ward order continuous functions [2] and investigated certain intersting results. The entire investigation is perform in (l)-group setting.

• Referencias bibliográficas
  • Y. Abramovich and G. Sirotkin, On order convergence of nets, Positivity 9 (2005), 287-292.
  • https://doi.org/10.1007/s11117-004-7543-x
  • D. Burton and J. Coleman, Quasi-Cauchy sequences, Amer. Math. Monthly 117, no. 4 (2010), 328-333.
  • https://doi.org/10.4169/000298910x480793
  • I. Canak and D. Mik, New types of continuity, Abstr. Appl. Anal. 2010 (2010), Article ID: 258980. [5]
  • H. Çakalli, Slowly oscillating continuity, Abstr. Appl. Anal. 2008 (2008), Article ID 485706.
  • https://doi.org/10.1155/2008/485706
  • H. Çakalli, Forward Continuity, J. Comput Anal. Appl. 13, no. 2 (2011), 225-230.
  • H. Çakalli, Statistical ward continuity, Applied Mathematics Letters 24 (2011), 1724-1728.
  • https://doi.org/10.1016/j.aml.2011.04.029
  • H. Çakalli, Statistical quasi-Cauchy sequences, Mathematical and Computer Modelling 54 (2011), 1620-1624.
  • https://doi.org/10.1016/j.mcm.2011.04.037
  • H. Çakalli and B. Haarika, Ideal quasi-Cauchy sequences, J. Inequal. Appl. 234 (2012), 1-11.
  • https://doi.org/10.1186/1029-242X-2012-234
  • R. Engelking, General topology, Sigma Ser. Pure Math., Heldermann, Berlin Vol. 6 2nd Edition (1989). [17]
  • H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244.
  • https://doi.org/10.4064/cm-2-3-4-241-244
  • J. A. Fridy, On stastistical convergence, Analysis 5 (1985), 301-313.
  • https://doi.org/10.1524/anly.1985.5.4.301
  • P. Kostyrko, T. Šalát and W. Wilczyński, $mathcal{I}$-convergence, Real Anal. Exchange. 26, no. 2 (2000/2001), 669-685.
  • https://doi.org/10.2307/44154069
  • I. J. Schoenberg, The integrability methods, Amer. Math. Monthly 66 (1959), 361-375.
  • https://doi.org/10.1080/00029890.1959.11989303
  • R. W. Vallin, Creating slowly oscillating sequences and slowly oscilating continuous functions, Acta. Math. Univ. Comenianae 25 (2011), 71-78