We introduce a space of sequences \( \ell_p^\lambda \) of nonabsolute type, which is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ≤ p < ∞; respectively. Further, we deduce some imbedding relations and construct a basis for the space \( \ell_p^\lambda \), where 1 ≤ p < ∞.
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References
B. Altay and F. Başar, “On some Euler sequence spaces of nonabsolute type,” Ukr. Math. J., 57, No. 1, 1–17 (2005).
B. Altay, F. Başar, and M. Mursaleen, “On the Euler sequence spaces which include the spaces ℓ p and ℓ∞,” Inform. Sci., 176, No. 10, 1450–1462 (2006).
C. Aydın and F. Başar, “On the new sequence spaces which include the spaces c 0 and c,” Hokkaido Math. J., 33, No. 2, 383–398 (2004).
C. Aydın and F. Başar, “Some new paranormed sequence spaces,” Inform. Sci., 160, No. 1–4, 27–40 (2004).
C. Aydın and F. Başar, “Some new difference sequence spaces,” Appl. Math. Comput., 157, No. 3, 677–693 (2004).
C. Aydın and F. Başar, “Some new sequence spaces which include the spaces ℓ p and ℓ∞,” Demonstr. Math., 38, No. 3, 641–656 (2005).
F. Başar and B. Altay, “On the space of sequences of p-bounded variation and related matrix mappings,” Ukr. Math. J., 55, No. 1, 136–147 (2003).
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press (1952).
S. G. Kreĭn, Ju. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators, Amer. Math. Soc., Providence, RI (1982).
I. J. Maddox, Elements of Functional Analysis, Cambridge Univ. Press, Cambridge (1988).
E. Malkowsky, “Recent results in the theory of matrix transformations in sequence spaces,” Mat. Vestnik, 49, 187–196 (1997).
E. Malkowsky and E. Savaş, “Matrix transformations between sequence spaces of generalized weighted means,” Appl. Math. Comput., 147, No. 2, 333–345 (2004).
M. Mursaleen, F. Bas¸ar, and B. Altay, “On the Euler sequence spaces which include the spaces ℓ p and ℓ∞ II,” Nonlinear Analysis: TMA, 65, No. 3, 707–717 (2006).
M. Mursaleen and A. K. Noman, “On the spaces of λ-convergent and bounded sequences,” Thai J. Math., 8, No. 2, 311–329 (2010).
M. Mursaleen and A. K. Noman, “On some new difference sequence spaces of nonabsolute type,” Math. Comput. Mod., 52, 603–617 (2010).
P.-N. Ng, “On modular space of a nonabsolute type,” Nanta Math., 2, 84–93 (1978).
P.-N. Ng and P.-Y. Lee, “Cesàro sequence spaces of nonabsolute type,” Comment. Math. Prace Mat., 20, No. 2, 429–433 (1978).
C.-S. Wang, “On Nörlund sequence spaces,” Tamkang J. Math., 9, 269–274 (1978).
A. Wilansky, Summability through Functional Analysis, North-Holland, Amsterdam (1984).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 489–501, April, 2011.
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Mursaleen, M., Noman, A.K. On some imbedding relations between certain sequence spaces. Ukr Math J 63, 564–579 (2011). https://doi.org/10.1007/s11253-011-0525-9
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DOI: https://doi.org/10.1007/s11253-011-0525-9