Mean convergence theorems to generalized acute points for generalized pseudocontractions

Yıl 2023, Cilt: 7 Sayı: 2, 387 - 404, 23.07.2023

Toshiharu Kawasaki

https://doi.org/10.31197/atnaa.1299905

Öz

Convergence theorems required more assumptions on parameters than fixed point theorems. In this paper we generalize the concept of acute point and we introduce some convergence theorems that holds under the same assumptions on parameters as fixed point theorems.

Anahtar Kelimeler

Mean convergence theorem, Generalized acute point, Generalized skew-acute point, Generalized pseudocontraction, Banach space

Kaynakça

• [1] S. Atsushiba, S. Iemoto, R. Kubota, and Y. Takeuchi, Convergence theorems for some classes of nonlinear mappings in Hilbert spaces, Linear and Nonlinear Analysis, 2 (2016), 125-153.
• [2] J.-B. Baillon, Un théorème de type ergodique pour les contractions non linéaires dans un espace de Hilbert, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. Séries A et B 280 (1975), 1511-1514.
• [3] F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, Journal of Mathematical Analysis and Applications 20 (1967), 197-228.
• [4] D. Butnariu, A. N. Iusem, and E. Resmerita, Total convexity for powers of the norm in uniformly convex Banach spaces, Journal of Convex Analysis 7 (2000), 319-334.
• [5] I. Ciornescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Mathematics and its applications, vol. 62, Kluwer Academic Publishers, Dordrecht, 1990.
• [6] T. Ibaraki and W. Takahashi, A new projection and convergence theorems for the projections in Banach spaces, J. Approx. Theory 149 (2007), 1-14.
• [7] T. Kawasaki, An extension of existence and mean approximation of fixed points of generalized hybrid non-self mappings in Hilbert spaces, preprint.
• [8] T. Kawasaki, Fixed points theorems and mean convergence theorems for generalized hybrid self mappings and non-self mappings in Hilbert spaces, Pacific Journal of Optimization 12 (2016), 133-150.
• [9] T. Kawasaki, Fixed point theorem for widely more generalized hybrid demicontinuous mappings in Hilbert spaces, Proceedings of Nonlinear Analysis and Convex Analysis, YokohamaPublishers, Yokohama, to appear.
• [10]T. Kawasaki, Fixed point theorems for widely more generalized hybrid mappings in metric spaces, anach spaces, and Hilbert spaces, Journal of Nonlinear and Convex Analysis 19 (2018), 1675-1683.
• [11] T. Kawasaki, On the convergence of orbits to a fixed point for widely more generalized hybrid mappings, Nihonkai Mathematical Journal 27 (2016), 89-97.
• [12]T. Kawasaki, Fixed point theorems for widely more generalized hybrid mappings in a metric space, a Banach space, and a Hilbert space, Journal of Nonlinear and Convex Analysis, 19 (2018), 1675-1683.
• [13] T. Kawasaki, Fixed point and acute point theorems for new mappings in a Banach space, Journal of Mathematics 2019 (2019), 12 pages.
• [14] T. Kawasaki, Mean convergence theorems for new mappings in a Banach space, Journal of Nonlinear and Variational Analysis 3 (2019), 61-78.
• [15]T. Kawasaki, Fixed point and acute point theorems for generalized pseudo contractions in a Banach space, Proceedings of Nonlinear Analysis and Convex Analysis, Yokohama Publishers, Yokohama, submitted.
• [16] T. Kawasaki, Weak convergence theorems for new mappings in a Banach space, Linear and Nonlinear Analysis 5 (2019), 147-171. [17] T. Kawasaki, Generalized acute point theorems for generalized pseudocontractions in a Banach space, Linear and Nonlinear Analysis 6 (2020), 73-90.
• [18] T. Kawasaki and T. Kobayashi, Existence and mean approximation of fixed points of generalized hybrid non-self mappings in Hilbert spaces, Scientiae Mathematicae Japonicae 77 (Online Version: e-2014) (2014), 13-26 (Online Version: 29-42)
• [19] T. Kawasaki and W. Takahashi, Existence and mean approximation of fixed points of generalized hybrid mappings in Hilbert spaces, Journal of Nonlinear and Convex Analysis 14 (2013), 71-87.
• [20] T. Kawasaki and W. Takahashi, Fixed point and nonlinear ergodic theorems for widely more generalized hybrid mappings in Hilbert spaces and applications, Proceedings of Nonlinear Analysis and Convex Analysis, Yokohama Publishers, Yokohama, to appear.
• [21] T. Kawasaki and W. Takahashi, Fixed point theorems for generalized hybrid demicontinuous mappings in Hilbert spaces, Linear and Nonlinear Analysis 1 (2015), 12-138.
• [22] P. Kocourek, W. Takahashi, and J.-C. Yao, Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese Journal of Mathematics 14 (2010), 2497-2511.
• [23] F. Kohsaka and W. Takahashi, Generalized nonexpansive retractions and a proximal type algorithm in Banach spaces, Journal of Nonlinear and Convex Analysis 8 (2007), 197-209.
• [24] F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Archiv der Mathematik 91 (2008), 166-177.
• [25] W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000.
• [26] W. Takahashi, Fixed point theorems for new nonlinear mappings in a Hilbert space, Journal of Nonlinear and Convex Analysis 11 (2010), 79-88.
• [27] W. Takahashi and Y. Takeuchi, Nonlinear ergodic theorem without convexity for generalized hybrid mappings in a Hilbert space, Journal of Nonlinear and Convex Analysis 12 (2011), 399-406.
• [28] W. Takahashi, N.-C. Wong, and J.-C. Yao, Attractive point and mean convergence theorems for new generalized non-spreading mappings in Banach spaces, Infinite Products of Operators and Their Applications (S. Reich and A. J. Zaslavski, eds.), Contemporary Mathematics, vol. 636, American Mathematical Society, Providence, 2015, pp. 225-248.