Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 9 Sayı: 2, 27 - 36, 31.12.2023

Veysel Nezir Nizami Mustafa

Öz

Kaynakça

  • 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.

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

Yıl 2023, Cilt: 9 Sayı: 2, 27 - 36, 31.12.2023

Veysel Nezir Nizami Mustafa

Öz

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.

Anahtar Kelimeler

Fixed point property nonexpansive mapping Köthe-Toeplitz dual

Kaynakça

  • 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.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Veysel Nezir 0000-0001-9640-8526

Nizami Mustafa 0000-0002-2758-0274

Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 2 Kasım 2023
Kabul Tarihi 31 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 9 Sayı: 2

Kaynak Göster

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.
AMA 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. Aralık 2023;9(2):27-36.
Chicago Nezir, Veysel, ve 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 9, sy. 2 (Aralık 2023): 27-36.
EndNote Nezir V, Mustafa N (01 Aralık 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 V. Nezir ve 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, c. 9, sy. 2, ss. 27–36, 2023.
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 (Aralık 2023), 27-36.
JAMA 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 ve 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, c. 9, sy. 2, 2023, ss. 27-36.
Vancouver 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.