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THE SPACES OF CESRO almost CONVERGENT SEQUENCES AND CORE THEOREMS

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Acta Mathematica Scientia 2012年第6期32卷 2265-2278页

作者： Kuddusi Kayaduman Mehmet Sengönül Science and Art Faculty Gaziantep UniversityGaziantep/Turkey Science and Art Faculty Nev sehir UniversityNev sehir/Turkey

As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.

关键词： almost convergence matrix domain of a sequence space β- and γ-duals andmatrix transformations core theorems isomorphism

DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r,s) ON SOME MADDOX'S SPACES

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Acta Mathematica Scientia 2014年第2期34卷 394-408页

作者： Faruk OZGER Feyzi BASAR Department of Mathematics Fatih UniversityHadomky Campus

The domain of generalized difference matrix B（r, s） in the classical spaces L∞, e, and co was recently studied by Kirisci and Basar in [16]. The main goal of this article is to introduce the paranormed sequence spaces L∞（B,p）, c（B,p）, and co（B,p）, which are more general and comprehensive than the corresponding consequences of the matrix domain of B（r, s）, as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces L∞ （B, p）, c（B, p）, and co （B, p） are computed and the bases of the spaces c（B, p） and co （B, p） are constructed. The final section of this article is devoted to the characterization of the classes （λ（B, p）： μ） and （μ：λ（B, p））, where λ ∈ {c, co, L∞ } and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of Mmost convergent sequences is obtained by means of a given lemma.

关键词： Matrix domain double sequential band matrices almost convergence para-normed spaces matrix transformations

The Equivalence of Two Convergent Sequence of Bounded Sequences in Normed Space

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Journal of Mathematical Research and Exposition 2009年第3期29卷 568-570页

作者： WANG Rui Dong School of Mathematical Sciences Nankai University Tianjin 300071 China Department of Mathematics Tianjin University of Technology Tianjin 300191 China

Two kinds of convergent sequences on the real vector space m of all bounded sequences in a real normed space X were discussed in this paper, and we prove that they are equivalent, which improved the results of [1].

关键词： almost convergence quasi-almost convergence.