Statistical Relative Uniform Convergence in Dually Residuated Lattice Totally Ordered Semigroups
DOI:
https://doi.org/10.5644/SJM.15.02.07Keywords:
Dually Residuated Lattice Ordered Semigroup, Relatively Uniform Convergence, Statistical ConvergenceAbstract
We define the notions of statistical relative uniform convergence and statistical relative uniform Cauchy in dually residuated lattice totally ordered semigroups (simply, DRlt-semigroups). Then, we give some basic properties for statistically relatively uniform convergent sequences. Also, we introduce statistical relative uniform limit points and cluster points in DRlt-semigroups, then the relations between these and limit points of the sequence are given.
Downloads
References
J Connor: The statistical and strong p-Cesaro convergence of sequences, Analysis 8 (1988) 47-63.
J. Connor, J. Kline: On Statistical Limit Points and the Consistency of Statistical Convergence, J. Math. Anal. Appl. 197 (1996) 392--399.
J.A. Fridy: On statistical convergence, Analysis 5 (1985), 301-313.
J.A. Fridy: Statistical limit points, Proc. Amer. Math. Soc. 118(4) (1993) 1187-1192.
J.A. Fridy and C. Orhan: Lacunary statistical convergence, Pacific J. Math. 160 (1993) 43--51.
M. Jasem: Relatively Uniform Convergence In Dually Residuated Lattice Ordered Semigroups, Aplimat (2011) 129-136.
E. Kolk: Matrix Summability of Statistically Convergent Sequences, Analysis 13 (1993) 77-83.
H. Steinhaus: Sur la convergence ordinaire et la convergence asymptotique, Collog. Math. 2 (1951) 73-74.
K. L. N. Swamy: Dually Residuated Lattice Ordered Semigroups, Math. Annalen, 159 (1965) 105-114.
K. L. N. Swamy: Dually Residuated Lattice Ordered Semigroups, II, Math. Annalen, 160 (1965) 64-71.
K. L. N. Swamy: Dually Residuated Lattice Ordered Semigroups, III, Math. Annalen, 167 (1966) 71-74.
