In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. | Turk J Math (2016) 40: 1134 – 1143 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Some results concerning the summability of spliced sequences 1 2,∗ ˙ 1 , Mehmet UNVER ¨ Tu˘ gba YURDAKADIM Department of Mathematics, Faculty of Arts and Sciences, Hitit University, Ulukavak, C ¸ orum, Turkey 2 Department of Mathematics, Faculty of Science, Ankara University, Tando˘ gan, Ankara, Turkey Received: • Accepted/Published Online: • Final Version: Abstract: A spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. We also present some further results via the Lebesgue integral. Key words: Matrix summability, spliced sequences, A -density, core of a sequence 1. Introduction In 1930, the core of a sequence that is strongly related to the set of limit points of the sequence was introduced by Knopp [10] and several properties of this concept have been studied since then. Particularly papers that investigate under which conditions the core of the transformation of a sequence by a summability matrix is a subset of the core of the original sequence have been written by many authors [1, 2, 6, 9, 12, 13]. In the present paper we give some inequalities that are closely connected to the core of the transformation of a spliced sequence by a summability matrix. Recently Osikiewicz [14] studied the summability of spliced sequences. He has shown that A -limits of spliced sequences are closely related to A -densities of the sets in the partition. Furthermore, Unver et al. [16] have investigated the summability of spliced sequences in
