Araştırma Makalesi
Yıl 2023,
Cilt: 12 Sayı: 1, 55 - 64, 30.04.2023
Öz
Kaynakça
- K. Aoyama, F. Kohsaka, Fixed point theorem for $\alpha$-nonexpansive mappings in Banach spaces, Nonlinear Analysis 74 (13) (2011) 4378-4391.
- J. Garcia-Falset, E. Llorens-Fuster, T. Suzuki, Fixed point theory for A class of generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications 375 (1) (2011) 185-195.
- R. Pandey, R. Pant, W. Rakocevic, R. Shukla, Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications, Results in Mathematics 74 (1) (2019) Article Number 7 24 pages.
- R. Pant, R. Shukla, Approximating fixed points of generalized $\alpha$-nonexpansive mappings in Banach spaces, Numerical Functional Analysis and Optimization 38 (2) (2017) 248-266.
- T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications 340 (2) (2008) 1088-1095.
- S. Temir, Convergence theorems for a general class of nonexpansive mappings in Banach spaces, International Journal of Nonlinear Analysis and Applications (in press).
- G. I. Usurelu, A. Bejenaru, M. Postolache, Operators with property (E) as concerns numerical analysis and visualization, Numerical Functional Analysis and Optimization 41 (11) (2020) 1398-1419.
- İ. Yıldırım, On fixed point results for mixed nonexpansive mappings, in: F. Yılmaz, A. Queiruga-Dios, M. J. Santos S\'anchez, D. Rasteiro, V. Gayoso Mart\'inez, J. Mart\'in Vaquero (Eds.), Mathematical Methods for Engineering Applications, Vol. 384 of Springer Proceedings in Mathematics and Statistics, Springer, Cham, 2022, pp. 191-198.
- İ. Yıldırım, N. Karaca, Generalized $(\alpha,\beta)$-nonexpansive multivalued mappings and their properties, in: B. Gürbulak, H. Özkan (Eds.), International Congress on Natural Sciences, Erzurum, 2021, pp. 672-679.
- N. Hussain, K. Ullah, M. Arshad, Fixed point approximation of Suzuki generalized non-expansive mappings via new faster iteration process, Journal of Nonlinear and Convex Analysis 19 (8) (2018) 1383-1393.
- B. S. Thakur, D. Thakur, M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings, Applied Mathematics and Computation 275 (2016) 147-155.
- S. Temir, Weak and strong convergence theorems for three Suzuki's generalized nonexpansive mappings, Publications de l'Institut Mathematique 110 (124) (2021) 121-129.
- K. Ullah and M. Arshad, Numerical reckoning fixed points for Suzuki's generalized nonexpansive mappings via new iteration process, Filomat 32 (1) (2018) 187-196.
- G. I. Usurelu, M. Postolache, Convergence analysis for a three-step Thakur iteration for Suzuki-type nonexpansive mappings with visualization, Symmetry 11 (12) (2019) 1-18.
- S. Temir, Ö. Korkut, Some convergence results using a new iteration process for generalized nonexpansive mappings in Banach spaces, Asian-European Journal of Mathematics 16 (05) 2350077 (2023).
- J. A. Clarkson, Uniformly convex spaces, Transactions of the American Mathematical Society 40 (3) (1936) 396-414.
- Z. Opial, Weak convergence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society 73 (4) (1967) 591-597.
- M. Edelstein, Fixed point theorems in uniformly convex Banach spaces, Proceedings of the American Mathematical Society 44 (2) (1974) 369-374.
- J. Schu, Weak and strong convergence of fixed points of asymptotically nonexpansive mappings, Bulletin of the Australian Mathematical Society 43 (1) (1991) 153-159.
- H. F. Senter, W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proceedings of the American Mathematical Society 44 (2) (1974) 375-380.
Yıl 2023,
Cilt: 12 Sayı: 1, 55 - 64, 30.04.2023
Öz
This paper studies the convergence of fixed points for Garsia-Falset generalized nonexpansive mappings. First, it investigates weak and strong convergence results for Garsia-Falset generalized nonexpansive mappings using the Temir-Korkut iteration in uniformly convex Banach spaces. This paper then exemplifies Garsia-Falset generalized nonexpansive mappings, which exceed the class of Suzuki generalized nonexpansive mappings. Moreover, it numerically compares this iteration's convergence speed with the well-known Thakur iteration of approximating the fixed point of Garsia-Falset generalized nonexpansive mapping. The results show that the Temir-Korkut iteration converges faster than the Thakur iteration converges. Finally, this paper discusses the need for further research.
Anahtar Kelimeler
Generalized nonexpansive mapping Fixed point Uniformly-convex Banach spaces
Kaynakça
- K. Aoyama, F. Kohsaka, Fixed point theorem for $\alpha$-nonexpansive mappings in Banach spaces, Nonlinear Analysis 74 (13) (2011) 4378-4391.
- J. Garcia-Falset, E. Llorens-Fuster, T. Suzuki, Fixed point theory for A class of generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications 375 (1) (2011) 185-195.
- R. Pandey, R. Pant, W. Rakocevic, R. Shukla, Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications, Results in Mathematics 74 (1) (2019) Article Number 7 24 pages.
- R. Pant, R. Shukla, Approximating fixed points of generalized $\alpha$-nonexpansive mappings in Banach spaces, Numerical Functional Analysis and Optimization 38 (2) (2017) 248-266.
- T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications 340 (2) (2008) 1088-1095.
- S. Temir, Convergence theorems for a general class of nonexpansive mappings in Banach spaces, International Journal of Nonlinear Analysis and Applications (in press).
- G. I. Usurelu, A. Bejenaru, M. Postolache, Operators with property (E) as concerns numerical analysis and visualization, Numerical Functional Analysis and Optimization 41 (11) (2020) 1398-1419.
- İ. Yıldırım, On fixed point results for mixed nonexpansive mappings, in: F. Yılmaz, A. Queiruga-Dios, M. J. Santos S\'anchez, D. Rasteiro, V. Gayoso Mart\'inez, J. Mart\'in Vaquero (Eds.), Mathematical Methods for Engineering Applications, Vol. 384 of Springer Proceedings in Mathematics and Statistics, Springer, Cham, 2022, pp. 191-198.
- İ. Yıldırım, N. Karaca, Generalized $(\alpha,\beta)$-nonexpansive multivalued mappings and their properties, in: B. Gürbulak, H. Özkan (Eds.), International Congress on Natural Sciences, Erzurum, 2021, pp. 672-679.
- N. Hussain, K. Ullah, M. Arshad, Fixed point approximation of Suzuki generalized non-expansive mappings via new faster iteration process, Journal of Nonlinear and Convex Analysis 19 (8) (2018) 1383-1393.
- B. S. Thakur, D. Thakur, M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings, Applied Mathematics and Computation 275 (2016) 147-155.
- S. Temir, Weak and strong convergence theorems for three Suzuki's generalized nonexpansive mappings, Publications de l'Institut Mathematique 110 (124) (2021) 121-129.
- K. Ullah and M. Arshad, Numerical reckoning fixed points for Suzuki's generalized nonexpansive mappings via new iteration process, Filomat 32 (1) (2018) 187-196.
- G. I. Usurelu, M. Postolache, Convergence analysis for a three-step Thakur iteration for Suzuki-type nonexpansive mappings with visualization, Symmetry 11 (12) (2019) 1-18.
- S. Temir, Ö. Korkut, Some convergence results using a new iteration process for generalized nonexpansive mappings in Banach spaces, Asian-European Journal of Mathematics 16 (05) 2350077 (2023).
- J. A. Clarkson, Uniformly convex spaces, Transactions of the American Mathematical Society 40 (3) (1936) 396-414.
- Z. Opial, Weak convergence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society 73 (4) (1967) 591-597.
- M. Edelstein, Fixed point theorems in uniformly convex Banach spaces, Proceedings of the American Mathematical Society 44 (2) (1974) 369-374.
- J. Schu, Weak and strong convergence of fixed points of asymptotically nonexpansive mappings, Bulletin of the Australian Mathematical Society 43 (1) (1991) 153-159.
- H. F. Senter, W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proceedings of the American Mathematical Society 44 (2) (1974) 375-380.
Toplam 20 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Nisan 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 12 Sayı: 1 |
Kaynak Göster
EBSCO |
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