Measure of Noncompactness of Matrix Operators on Some New Difference Sequence Spaces of Order mth

Year 2012, Volume: 1 Issue: 1, 50 - 70, 01.01.2012

Serkan Demiriz

Abstract

Kızmaz [13] studied the difference sequence spaces ℓ∞(∆), c(∆) and c(∆)

Keywords

Difference sequence spaces of order m, α−, β− and γ− dual

References

• Ahmad Z.U. and Mursaleen M., Kthe-Toeplitz duals of some new sequence spaces and their matrix maps, Publ. Inst. Math. 42(1987), 57-61.
• Altay B., On the space of p− summable difference sequences of order m, (1 ≤ p < ∞). Studia Sci. Math. Hungar 43(4)(2006), 387-402.
• Altay B. and Ba¸sar F. and Mursaleen M., On the Euler sequence spaces which include the spaces ℓpand ℓ∞II, Inform. Sci. 176(2006), 1450-1462.
• Altay B. and Ba¸sar F., Some Euler sequence spaces of non-absolute type, Ukrainian Math. J. 57(1)(2005), 1-17.
• Altay B. and Ba¸sar F., On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26(2002), 701-715.
• Aydın C. and Ba¸sar F., On the new sequence spaces which include the spaces c0and c, Hokkaido Math. J. 33(2004), 383-398.
• Aydın C. and Ba¸sar F., Some new difference sequence spaces, Appl. Math. Comput. 157(2004), 677-693.
• Ba¸sar F. and Altay B., On the space of sequences of p− bounded variation and related matrix mappings, Ukrainian Math. J. 55(2003), 136-147.
• C¸ olak R, Et M, Malkowsky E. Some topics of sequence spaces, In: Lecture Notes in Mathematics, Fırat Univ Elazı˜g, Turkey, 2004.1-63, Fırat Univ. Press, 2004, ISBN:975-394-0386-6
• C¸ olak R. and Et M., On some generalized difference sequence spaces and related matrix transformations, Hokkaido Math. J. 26(3)(1997), 483-492.
• Demiriz S. and C¸ akan C., On some new paranormed Euler sequence spaces and Euler core , Acta Math. Sin. (Engl. Ser.),26(7)(2010), 1207-1222.
• Jarrah A. M. and Malkowsky E., Ordinary, absolute and strong summability and matrix transformations, Filomat 17(2003), 59-78.
• Kızmaz H., On certain sequence spaces, Canad. Math. Bull. 24(2)(1981), 169-176.
• M. Mursaleen, A.K.Noman, Applications of the Hausdorff measure of noncompactness in some sequence spaces of weighted means, Comput. Math. Appl. 60(2010),1245- 1258.
• M. Mursaleen, V. Karakaya, H. Polat, N. S¸im¸sek, Meausre of noncompactness of matrix operators on some difference sequence spaces of weighted means, Comput. Math. Appl. 62(2011),814-820.
• E. Evren Kara, M. Ba¸sarır, On compact operators and some Euler B(m)-difference sequence spaces, J. Math. Anal. Appl. 379(2011),499-511.
• Maddox I.J., Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phios. Soc. 64(1968), 335-340.
• Malkowsky E. and Parashar S.D., Matrix transformations in space of bounded and convergent difference sequence of order m, Analysis 17(1997), 87-97.
• Malkowsky E., Recent results in the theory of matrix transformations in sequence spaces, Mat. Vesnik 49(1997), 187-196.
• Malkowsky E. and Rakocevic V., An introduction into the theory of sequence spaces and measure of noncompactness, in: Zb. Rad. (Beogr), Vol. 9(17), Matematicki in- stitut SANU, Belgrade, (2000), 143-234.
• Malkowsky E. and Rakocevic V. and Zivkovic S., Matrix transformations between 0the sequence spaces wp
• Comput. 147(2004), 377-396.
• (Λ), vp(Λ), c0(Λ), 1 < p < ∞, and BK- spaces, Appl. Math. [22] Malkowsky E., Klassen von Matrixabbildungen in paranormierten FK-R¨aumen, Analysis (Munich) (7) (1987), 275-292.
• Ng P.-N. and Lee P.-Y., Ces`aro sequences spaces of non-absolute type, Comment Math. Prace Mat. 20(2)(1978), 429-433.
• Rakocevic V., Funkcionalna analiza, Naucna knjiga, Belgrad, 1994.
• Rakocevic V., Measures of noncompactness and some applications, Filomat 12(1998) 87-120.
• Stieglitz M. and Tietz H., Matrix transformationen von folgenr¨aumen eine ergeb- nis¨ubersicht, Math. Z. 154 (1977), 1-16.
• Wang C.-S., N¨orlund sequence spaces, Tamkang J. Math. 9(1978), 269-274.
• Wilansky A., Summability through Functional Analysis, North-Holland Mathematics Studies , Amsterdam, 85 1984.