Research Article
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A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces with Fixed Point Property

Year 2023, Volume: 9 Issue: 2, 27 - 36, 31.12.2023

Veysel Nezir , Nizami Mustafa

https://izlik.org/JA94AC85PN

Abstract

In the present study, we consider the Köthe-Toeplitz duals for the 2nd order and 3rd order types difference sequence space generalizations by Et and Esi studied in 2000. We work on Goebel and Kuczumow analogy for those spaces to obtain large classes of closed, bounded and convex subsets satisfying the fixed point property. In the study, we also study some other Banach spaces in connection with the Köthe-Toeplitz duals for the 2nd order and 3rd order generalized difference sequence spaces.

Keywords

Fixed point property nonexpansive mapping Köthe-Toeplitz dual

References

  • BEKTAŞ, Ç. A., ET, M., & ÇOLAK, R. (2004). Generalized difference sequence spaces and their dual spaces. Journal of Mathematical Analysis and Applications, 292(2): 423-432.
  • BROWDER, F. E. (1965). Fixed-point theorems for noncompact mappings in Hilbert space. Proceedings of the National Academy of Sciences, 53(6): 1272-1276.
  • CHEN, S., CUI, Y., HUDZIK, H., & SIMS, B. (2001). Geometric properties related to fixed point theory in some Banach function lattices. In Handbook of metric fixed point theory. Springer, Dordrecht, 339-389.
  • CUI, Y. (1999). Some geometric properties related to fixed point theory in Cesàro spaces. Collectanea Mathematica, 277-288.
  • CUI, Y., HUDZIK, H., & LI, Y. (2000). On the Garcfa-Falset Coefficient in Some Banach Sequence Spaces. In Function Spaces. CRC Press, 163-170.
  • CUI, Y., MENG, C., & PŁUCIENNIK, R. (2000). Banach—Saks Property and Property (β) in Cesàro Sequence Spaces. Southeast Asian Bulletin of Mathematics, 24(2):201-210.
  • ÇOLAK, R. (1989). On some generalized sequence spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 38: 35-46.
  • ET, M. (1996). On some generalized Cesàro difference sequence spaces. İstanbul University Science Faculty The Journal Of Mathematics, Physics and Astronomy, 55:221-229.
  • ET, M., & ÇOLAK, R. (1995). On some generalized difference sequence spaces. Soochow journal of mathematics, 21(4):377-386.
  • ET, M., & ESI, A. (2000). On Köthe-Toeplitz duals of generalized difference sequence spaces. Bull. Malays. Math. Sci. Soc, 23(1): 25-32.
  • EVEREST, T. M. (2013). Fixed points of nonexpansive maps on closed, bounded, convex sets in l1 (Doctoral dissertation, University of Pittsburgh).
  • FALSET, J. G. (1997). The fixed point property in Banach spaces with the NUS-property. Journal of Mathematical Analysis and Applications, 215(2):532-542.
  • GOEBEL, K., & KIRK, W. A. (1990). Topics in metric fixed point theory (No. 28). Cambridge university press.
  • GOEBEL, K., & KUCZUMOW, T. (1979). Irregular convex sets with fixed-point property for nonexpansive mappings. Colloquium Mathematicum, 2(40): 259-264.
  • KACZOR, W., & PRUS, S. (2004). Fixed point properties of some sets in l1. In Proceedings of the International Conference on Fixed Point Theory and Applications, 11p.
  • KIZMAZ, H. (1981). On certain sequence spaces. Canadian mathematical bulletin, 24(2):169-176.
  • KIRK, W. A. (1965). A fixed point theorem for mappings which do not increase distances. The American mathematical monthly, 72(9):1004-1006.
  • LIN, P. K. (2008). There is an equivalent norm on ℓ1 that has the fixed point property. Nonlinear Analysis: Theory, Methods & Applications, 68(8):2303-2308.
  • HERNÁNDEZ-LINARES, C. A., & JAPÓN, M. A. (2012). Renormings and fixed point property in non-commutative L1-spaces II: Affine mappings. Nonlinear Analysis: Theory, Methods & Applications, 75(13):5357-5361.
  • LINDENSTRAUSS, J., & TZAFRIRI, L. (1977). Classical Banach Spaces. Pt. 1. Sequence Spaces. Springer.
  • NGPENG-NUNG, N. N., & LEEPENG-YEE, L. Y. (1978). Cesàro sequence spaces of nonabsolute type. Commentationes mathematicae, 20(2):429–433.
  • ORHAN, C. (1983). Casaro Differance Sequence Spaces and Related Matrix Transformations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 32:55-63.
  • SCHAUDER, J. (1930). Der fixpunktsatz in funktionalraümen. Studia Mathematica, 2(1), 171-180.
  • SHIUE, J. S. (1970). On the Cesaro sequence spaces. Tamkang J. Math, 1(1):19-25.
  • TRIPATHY, B. C., ESI, A., & TRIPATHY, B. (2005). On new types of generalized difference Cesaro sequence spaces. Soochow Journal of Mathematics, 31(3):333-340.

Year 2023, Volume: 9 Issue: 2, 27 - 36, 31.12.2023

Veysel Nezir , Nizami Mustafa

https://izlik.org/JA94AC85PN

Abstract

References

  • BEKTAŞ, Ç. A., ET, M., & ÇOLAK, R. (2004). Generalized difference sequence spaces and their dual spaces. Journal of Mathematical Analysis and Applications, 292(2): 423-432.
  • BROWDER, F. E. (1965). Fixed-point theorems for noncompact mappings in Hilbert space. Proceedings of the National Academy of Sciences, 53(6): 1272-1276.
  • CHEN, S., CUI, Y., HUDZIK, H., & SIMS, B. (2001). Geometric properties related to fixed point theory in some Banach function lattices. In Handbook of metric fixed point theory. Springer, Dordrecht, 339-389.
  • CUI, Y. (1999). Some geometric properties related to fixed point theory in Cesàro spaces. Collectanea Mathematica, 277-288.
  • CUI, Y., HUDZIK, H., & LI, Y. (2000). On the Garcfa-Falset Coefficient in Some Banach Sequence Spaces. In Function Spaces. CRC Press, 163-170.
  • CUI, Y., MENG, C., & PŁUCIENNIK, R. (2000). Banach—Saks Property and Property (β) in Cesàro Sequence Spaces. Southeast Asian Bulletin of Mathematics, 24(2):201-210.
  • ÇOLAK, R. (1989). On some generalized sequence spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 38: 35-46.
  • ET, M. (1996). On some generalized Cesàro difference sequence spaces. İstanbul University Science Faculty The Journal Of Mathematics, Physics and Astronomy, 55:221-229.
  • ET, M., & ÇOLAK, R. (1995). On some generalized difference sequence spaces. Soochow journal of mathematics, 21(4):377-386.
  • ET, M., & ESI, A. (2000). On Köthe-Toeplitz duals of generalized difference sequence spaces. Bull. Malays. Math. Sci. Soc, 23(1): 25-32.
  • EVEREST, T. M. (2013). Fixed points of nonexpansive maps on closed, bounded, convex sets in l1 (Doctoral dissertation, University of Pittsburgh).
  • FALSET, J. G. (1997). The fixed point property in Banach spaces with the NUS-property. Journal of Mathematical Analysis and Applications, 215(2):532-542.
  • GOEBEL, K., & KIRK, W. A. (1990). Topics in metric fixed point theory (No. 28). Cambridge university press.
  • GOEBEL, K., & KUCZUMOW, T. (1979). Irregular convex sets with fixed-point property for nonexpansive mappings. Colloquium Mathematicum, 2(40): 259-264.
  • KACZOR, W., & PRUS, S. (2004). Fixed point properties of some sets in l1. In Proceedings of the International Conference on Fixed Point Theory and Applications, 11p.
  • KIZMAZ, H. (1981). On certain sequence spaces. Canadian mathematical bulletin, 24(2):169-176.
  • KIRK, W. A. (1965). A fixed point theorem for mappings which do not increase distances. The American mathematical monthly, 72(9):1004-1006.
  • LIN, P. K. (2008). There is an equivalent norm on ℓ1 that has the fixed point property. Nonlinear Analysis: Theory, Methods & Applications, 68(8):2303-2308.
  • HERNÁNDEZ-LINARES, C. A., & JAPÓN, M. A. (2012). Renormings and fixed point property in non-commutative L1-spaces II: Affine mappings. Nonlinear Analysis: Theory, Methods & Applications, 75(13):5357-5361.
  • LINDENSTRAUSS, J., & TZAFRIRI, L. (1977). Classical Banach Spaces. Pt. 1. Sequence Spaces. Springer.
  • NGPENG-NUNG, N. N., & LEEPENG-YEE, L. Y. (1978). Cesàro sequence spaces of nonabsolute type. Commentationes mathematicae, 20(2):429–433.
  • ORHAN, C. (1983). Casaro Differance Sequence Spaces and Related Matrix Transformations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 32:55-63.
  • SCHAUDER, J. (1930). Der fixpunktsatz in funktionalraümen. Studia Mathematica, 2(1), 171-180.
  • SHIUE, J. S. (1970). On the Cesaro sequence spaces. Tamkang J. Math, 1(1):19-25.
  • TRIPATHY, B. C., ESI, A., & TRIPATHY, B. (2005). On new types of generalized difference Cesaro sequence spaces. Soochow Journal of Mathematics, 31(3):333-340.
There are 25 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Research Article
Authors

Veysel Nezir 0000-0001-9640-8526

Nizami Mustafa 0000-0002-2758-0274

Submission Date November 2, 2023
Acceptance Date December 31, 2023
Publication Date December 31, 2023
IZ https://izlik.org/JA94AC85PN
Published in Issue Year 2023 Volume: 9 Issue: 2

Cite

APA Nezir, V., & Mustafa, N. (2023). A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces with Fixed Point Property. Eastern Anatolian Journal of Science, 9(2), 27-36. https://izlik.org/JA94AC85PN
AMA 1.Nezir V, Mustafa N. A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces with Fixed Point Property. Eastern Anatolian Journal of Science. 2023;9(2):27-36. https://izlik.org/JA94AC85PN
Chicago Nezir, Veysel, and Nizami Mustafa. 2023. “A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces With Fixed Point Property”. Eastern Anatolian Journal of Science 9 (2): 27-36. https://izlik.org/JA94AC85PN.
EndNote Nezir V, Mustafa N (December 1, 2023) A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces with Fixed Point Property. Eastern Anatolian Journal of Science 9 2 27–36.
IEEE [1]V. Nezir and N. Mustafa, “A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces with Fixed Point Property”, Eastern Anatolian Journal of Science, vol. 9, no. 2, pp. 27–36, Dec. 2023, [Online]. Available: https://izlik.org/JA94AC85PN
ISNAD Nezir, Veysel - Mustafa, Nizami. “A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces With Fixed Point Property”. Eastern Anatolian Journal of Science 9/2 (December 1, 2023): 27-36. https://izlik.org/JA94AC85PN.
JAMA 1.Nezir V, Mustafa N. A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces with Fixed Point Property. Eastern Anatolian Journal of Science. 2023;9:27–36.
MLA Nezir, Veysel, and Nizami Mustafa. “A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces With Fixed Point Property”. Eastern Anatolian Journal of Science, vol. 9, no. 2, Dec. 2023, pp. 27-36, https://izlik.org/JA94AC85PN.
Vancouver 1.Veysel Nezir, Nizami Mustafa. A Large Class of Closed, Bounded and Convex Subsets in Köthe-Toeplitz Duals of Certain Generalized Difference Sequence Spaces with Fixed Point Property. Eastern Anatolian Journal of Science [Internet]. 2023 Dec. 1;9(2):27-36. Available from: https://izlik.org/JA94AC85PN