Yazar "Savasci, Medine Yesilkayagil" seçeneğine göre listele

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    DOMAIN OF THE CESARO MEAN OF ORDER ? IN MADDOX'S SPACE l(p)
    (Publications L Institut Mathematique Matematicki, 2023) Savasci, Medine Yesilkayagil; Basar, Feyzi
    The sequence space l(p) was defined by I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford (2), 18 (1967), 345-355. Here, we introduce the paranormed Cesaro sequence space l(C-alpha, p) of order alpha, of non-absolute type as the domain of Cesaro mean C-alpha of order alpha and prove that the spaces l (C-alpha, p) and l(p) are linearly paranorm isomorphic. Besides this, we compute the alpha-, beta- and gamma-duals of the space l(C-alpha, p) and construct the basis of the space l(C-alpha, p) together with the characterization of the classes of matrix transformations from the space l(C-alpha, p) into the spaces l(infinity) of bounded sequences and f of almost convergent sequences, and any given sequence space Y, and from a given sequence space Y into the sequence space l(C-alpha, p). Finally, we emphasize on some geometric properties of the space l(C-alpha, p).
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    The Hahn sequence space generated by the Cesaro mean of order m
    (Springer Birkhauser, 2024) Savasci, Medine Yesilkayagil; Basar, Feyzi
    Hahn (Math Phys 32:3-88, 1922) defined the sequence space h. The main purpose of this study is to introduce the new Hahn sequence space h(C-m) as the domain of Cesaro mean of order m and give some topological properties of the space h(Cm). Moreover, we determine the alpha-, beta-and gamma-duals of the space h(C-m) and characterize the classes (i1 : h), (h : 4), (h(C-m) : V-1) and (V-2 : h(Cm)) of matrix transformations, where 1 < p < infinity, V-1 is an element of {l(infinity), c, c(0), l(p)} and V-2 is any given sequence space. Finally, we compute the norm of the operators belonging to B(e(1), h(C-m)) and determine the Hausdorff measure of noncompactness of the operators in B(i(1), h(C-m)).
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    On the spaces of Cesaro absolutely p-summable, null and convergent sequences (vol 44, pg 3670, 2021)
    (Wiley, 2023) Savasci, Medine Yesilkayagil; Basar, Feyzi
    The sequence spaces l(p)(C-n), c(0)(C-n) and c(C-n) are introduced by Roopaei and Basar [8] as the domain of the Cesaro matrix C-n of order n in the spaces l(p), c(0) and c of absolutely p-summable, null and convergent sequences, respectively, where 0 < p < 1. As a direct consequence of incorrectly calculation of the inverse C-n of the Cesaro matrix C-n of order n, the main results in Sections 3 and 4 of Roopaei and Ba , sar [8] were wrongly obtained. The main purpose of this paper is to rectify the main results of [8] given in Sections 3 and 4.