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Sequences of Cesaro type using lacunary notion | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 114، دوره 13، شماره 2، مهر 2022، صفحه 1399-1405 اصل مقاله (389.18 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21237.2242 | ||
| نویسنده | ||
| Abdul Hamid Ganie* | ||
| Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University-Abha Male, 61421, Kingdom of Saudi Arabia | ||
| تاریخ دریافت: 10 شهریور 1399، تاریخ بازنگری: 05 شهریور 1400، تاریخ پذیرش: 13 شهریور 1400 | ||
| چکیده | ||
| The scenario of this article is to introduce the space $\mathfrak{R}^{t}_s(p, \Delta)$ based on a general Riesz sequence space. Its completeness property is derived and its linear isomorphism property with $\ell(p)$ is proved. The K\"{o}the-dual property of the space $\mathfrak{R}^{t}_s(p, \Delta)$ is also derived. Furthermore, its basis is constructed and some characterization of infinite matrices are given. | ||
| کلیدواژه‌ها | ||
| Ces`{a}ro sequences؛ lacunary sequences؛ Fr'{e}chet space | ||
| مراجع | ||
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[1] A.A. Albanese, J. Bonet and W.J. Ricker, Multiplier and averaging operators in the Banach spaces ces(p), 1 < p < ∞, Positivity 23 (2018), no. 1, 177–193. [2] A. Alexiewicz, On Cauchy’s condensation theorem, Studia Math. 16 (1957), 80—85 [3] A. Arhangelskii, Some types of factor mappings and the relations between classes of topological spaces, Soviet Math. Dokl. 4 (1963), 1726–1729. [4] I. Bala, On Ces`aro sequence space defined by a modulus function, Demonstr. Math. 45 (2012), no. 4, 157–163. [5] M. Ba¸sarir, Paranormed Ces`aro difference sequence space and related matrix transformation, Turk. J. Math. 15 (1991), 14–19. [6] G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc. 576 (1996). [7] G. P. Curbera and W. J. Ricker, Solid Extensions of the Ces`aro Operator on ℓp and c0, Integral Equations and Operator Theory 80 (2014), no. 1, 61–77.[8] E. D¨undar, N. Pancaroˇglu Akın, and U. Ulusu, Lacunary II-Invariant convergence of sequences of sets, Proc. Nat. Acad. Sci. India, Sect. A Phys. Sci. 91 (2021), 517–522. [9] M. Et, On some generalised Ces`aro difference sequence spaces, Istanbul Univ. Fen Fak. Mat. Derg. 55 (1996), 221–229. [10] D. Fathima and A.H. Ganie, On some new scenario of ∆- spaces, J. Nonlinear Sci. Appl. 14 (2021), 163–167. [11] A. R. Freedman, J.J. Sember and M. Raphael, Some Ces`aro type summability spaces, Proc. Lond. Math. Soc. 37 (1978), 508–520. [12] A.H. Ganie, New spaces over modulus function, Bol. Soc. Paranaense Mat. (in press), 1–6. [13] A.H. Ganie, Sigma bounded sequence and some matrix transformations, Algebra Lett. 3 (2013), 1–7. [14] A.H. Ganie and N.A. Sheikh, Matrix transformation into a new sequence space related to invariant means, Chamchuri J. Math., 4 (2012), 71–72. [15] D. Ghosh and P. D. Srivastava, On some vector valued sequence spaces defined using a modulus function, Indian J. Pure Appl. Math. 30 (1999), no. 8, 819–826. [16] A.A. Jagers, A note on Ces`aro sequence spaces, Nieuw. Arch. Wisk., 22 (1974), 113–124. [17] E. Kolk, Inclusion theorems for some sequence spaces defined by a sequence of modulli, Acta Comment. Univ. Tartu 970 (1994), 65–72. [18] G.M. Leibowitz, A note on the Ces`aro sequence spaces, Tamkang J. Math. 2 (1971), no. 2, 151–157. [19] W.A.J. Luxemburg and A.C. Zaanen, Some examples of normed K¨othe spaces, Math. Ann. 162 (1966), 337-–350. [20] I.J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Cam. Philos. Soc., 100 (1986), 161–166. [21] P.-N. Ng and P.-Y. Lee, Ces`aro sequences spaces of non-absolute type, Comment. Math. Prace Mat., 20 (1978), 429–433. [22] Programma van Jaarlijkse Prijsvragen (Annual Problem Section), Nieuw Arch. Wiskd. 16 (1968), 47–51. [23] W.H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 1973–1978. [24] E. Sava¸s, On some generalized sequence spaces defined by a modulus, Indian J. pure and Appl. Math. 30 (1999), 459–464. [25] J.S. Shiue, A note on the Ces`aro sequence space, Tamkang J. Math. 1 (1970), no. 2, 91–95. [26] H. Seng¨u, Some Ces`aro-type summability spaces defined by modulus function of order (α, β), Commun. Fac. Sci. Univ. Ank. Ser. A1 66 (2017), no. 2, 80–90. [27] U. Ulusu and F. Nuray, On the strongly lacunary summability of sequences of sets, J. Appl. Math. Bioinf. 3 (2013), no. 3, 75–88. | ||
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