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DOUBLE LACUNARY DENSITY AND LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES
(Akademiai Kiado Rt, 2010) Cakan, Celal; Altay, Bilal; Coskun, Huesamettin
In this paper, we have defined double lacunary density and investigated the relation between statistical and lacunary statistical convergence of double sequences. Also, we have solved an inequality related to the lacunary statistical limit superior of real bounded double sequences.
?-REGULAR MATRICES AND A ?-CORE THEOREM FOR DOUBLE SEQUENCES
(Hacettepe Univ, Fac Sci, 2009) Cakan, Celal; Altay, Bilal; Coskun, Huesamettin
The famous Knopp Core of a single sequence was extended to the P-core of a double sequence by R.F. Patterson. Recently, the MR-core and sigma-core of real bounded double sequences have been introduced and some inequalities analogues to those for Knoop's Core Theorem have been studied. The aim of this paper is to characterize a class of four-dimensional matrices, and so to obtain necessary and sufficient conditions for a new inequality related to the P- and sigma-cores.