Matrix characterization in double sequences and the core theorems

In this study, that is prepared as four chapter, after the definitions of a transformationsequence that is obtained with an infinite matrix, regularity, almost convergence,strongly regularity, almost regularity; the Knopp core and the Banach core of a boundedsequnce are defined and some covering theorems and results between these arealso presented in the first chapter.In the second chapter; in addition to the definitions of a double sequence and atransformation sequence that is obtained with a four dimentional matrix, regularity,almost convergence, strongly regularity, almost regularity, strongly almost regularityof a four dimentional matrix, the P-core and the MR-core of a double sequence aredefined.In the third chapter; ( c2? ,c2? )-regular, ( 2 2 f ,c? )-strongly regular, ( 2 2 c? , f )-almost regularand ( 2 2 f , f )-almost strongly regular matrix sets are characterized.In the fourth chapter; supposing x is a bounded double sequence, the properties ofa four dimentional matrix A should have, for the covering relations that is MR -Çek ( Ax) ? P -Çek (x) , MR -Çek ( Ax) ? MR -Çek (x) and P -Çek ( Ax) ? MR-Çek (x) to be hold are established.