Các n полynот ди abang liao peng s STst retSHA

Springer Science and Business Media LLC - Tập 2012 - Trang 1-14 - 2012
Shih-sen Chang1, Jong Kyu Kim2, Lin Wang1
1College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China
2Department of Mathematics Education, Kyungnam University, Masan, South Korea

Tóm tắt

Mục đích của bài báo này là điều chỉnh thuật toán lặp kiểu Halpern-Mann cho các nửa nhóm quasi-ϕ-asymptotically không mở rộng tổng quát để đạt được hội tụ mạnh dưới điều kiện giới hạn chỉ trong khuôn khổ của các không gian Banach. Các kết quả được trình bày trong bài báo nâng cao và mở rộng các kết quả gần đây tương ứng đã được nhiều tác giả công bố. MSC:47J05, 47H09, 49J25.

Từ khóa

#hội tụ mạnh #nửa nhóm #không gian Banach #quy trình lặp #thuật toán Halpern-Mann

Tài liệu tham khảo

Byrne C: A unified treatment of some iterative algorithms in signal processing and image construction. Inverse Probl. 2004, 20: 103–120. 10.1088/0266-5611/20/1/006 Combettes PL: The convex feasibility problem in image recovery. 95. In Advances in Imaging and Electron Physics. Academic Press, New York; 1996:155–270. Kitahara S, Takahashi W: Image recovery by convex combinations of sunny nonexpansive retractions. Topol. Methods Nonlinear Anal. 1993, 2: 333–342. Suzuki T: On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces. Proc. Am. Math. Soc. 2003, 131: 2133–2136. 10.1090/S0002-9939-02-06844-2 Xu HK: A strong convergence theorem for contraction semigroups in Banach spaces. Bull. Aust. Math. Soc. 2005, 72: 371–379. 10.1017/S000497270003519X Chang SS, Yang L, Liu JA: Strong convergence theorem for nonexpansive semi-groups in Banach spaces. Appl. Math. Mech. 2007, 28: 1287–1297. 10.1007/s10483-007-1002-x Zhang S: Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces. Appl. Math. Mech. 2009, 30(2):145–152. 10.1007/s10483-009-0202-y Chang SS, Lee HWJ, Chan CK: Convergence theorem of common fixed point for asymptotically nonexpansive semigroups in Banach spaces. Appl. Math. Comput. 2009, 212: 60–65. 10.1016/j.amc.2009.01.086 Cho SY, Kang SM: Approximation of fixed points of pseudocontraction semigroups based on a viscosity iterative process. Appl. Math. Lett. 2011, 24: 224–228. 10.1016/j.aml.2010.09.008 Cho YJ, Ciric L, Wang S:Convergence theorems for nonexpansive semigroups in CAT(0) spaces. Nonlinear Anal. 2011. doi:10.1016/j.na.2011.05.082 Thong DV: An implicit iteration process for nonexpansive semigroups. Nonlinear Anal. 2011. doi:10.1016/j.na.2011.05.090 Buong N: Hybrid Ishikawa iterative methods for a nonexpansive semigroup in Hilbert space. Comput. Math. Appl. 2011, 61: 2546–2554. 10.1016/j.camwa.2011.02.047 Mann WR: Mean value methods in iteration. Proc. Am. Math. Soc. 1953, 4: 506–510. 10.1090/S0002-9939-1953-0054846-3 Halpern B: Fixed points of nonexpanding maps. Bull. Am. Math. Soc. 1967, 73: 957–961. 10.1090/S0002-9904-1967-11864-0 Qin XL, Cho YJ, Kang SM, Zhou HY: Convergence of a modified Halpern-type iterative algorithm for quasi- ϕ -nonexpansive mappings. Appl. Math. Lett. 2009, 22: 1051–1055. 10.1016/j.aml.2009.01.015 Wang ZM, Su YF, Wang DX, Dong YC: A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces. J. Comput. Appl. Math. 2011, 235: 2364–2371. 10.1016/j.cam.2010.10.036 Matsushita S, Takahashi W: A strong convergence theorem for relatively nonexpansive mappings in Banach spaces. J. Approx. Theory 2005, 134: 257–266. 10.1016/j.jat.2005.02.007 Nakajo K, Takahashi W: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl. 2003, 279: 372–379. 10.1016/S0022-247X(02)00458-4 Nilsrakoo W, Sajung S: Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces. Appl. Math. Comput. 2011, 217(14):6577–6586. 10.1016/j.amc.2011.01.040 Su YF, Xu HK, Zhang X: Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications. Nonlinear Anal. 2010, 73: 3890–3906. 10.1016/j.na.2010.08.021 Kang J, Su Y, Zhang X: Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications. Nonlinear Anal. Hybrid Syst. 2010, 4(4):755–765. 10.1016/j.nahs.2010.05.002 Chang SS, Chan CK, Lee HWJ: Modified block iterative algorithm for quasi- ϕ -asymptotically nonexpansive mappings and equilibrium problem in Banach spaces. Appl. Math. Comput. 2011, 217: 7520–7530. 10.1016/j.amc.2011.02.060 Chang SS, Lee HWJ, Chan CK: A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications. Nonlinear Anal. TMA 2010, 73: 2260–2270. 10.1016/j.na.2010.06.006 Blum E, Oettli W: From optimization and variational inequalities to equilibrium problems. Math. Stud. 1994, 63(1/4):123–145. Yao Y, Cho YJ, Liou Y-C: Hierarchical convergence of an implicit double-net algorithm for nonexpansive semigroups and variational inequalities. Fixed Point Theory Appl. 2011., 2011: Article ID 101. doi:10.1186/1687–1812–2011–101 Yao Y, Shahzad N: New methods with perturbations for non-expansive mappings in Hilbert spaces. Fixed Point Theory Appl. 2011., 2011: Article ID 79. doi:10.1186/1687–1812–2011–79 Yao Y, Liou Y-C, Wong M-M, Yao J-C: Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems. Fixed Point Theory Appl. 2011., 2011: Article ID 53. doi:10.1186/1687–1812–2011–53 Yao Y, Chen R: Regularized algorithms for hierarchical fixed-point problems. Nonlinear Anal. 2011, 74: 6826–6834. 10.1016/j.na.2011.07.007 Yao Y, Shahzad N: Strong convergence of a proximal point algorithm with general errors. Optim. Lett. 2012. doi:10.1007/s11590–011–0286–2 Chang S, Wang L, Tang Y-K, Zao Y-H, Ma ZL: Strong convergence theorems of nonlinear operator equations for countable family of multi-valued total quasi- ϕ -asymptotically nonexpansive mappings with applications. Fixed Point Theory Appl. 2012., 2012: Article ID 69. doi:10.1186/1687–1812–2012–69 Qin X, Agarwal RP, Cho SY, Kang SM: Convergence of algorithms for fixed points of generalized asymptotically quasi-phi-nonexpansive mappings with applications. Fixed Point Theory Appl. 2012., 2012: Article ID 58. doi:10.1186/1687–1812–2012–58 Kim JK: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of asymptotically quasi- ϕ -nonexpansive mappings. Fixed Point Theory Appl. 2012., 2011: Article ID 10. doi:10.1186/1687–1812–10 Chang S, Kim JK, Lee HWJ, Chan CK: A generalization and improvement of Chidume theorems for total asymptotically nonexpansive mappings in Banach spaces. J. Inequal. Appl. 2012., 2012: Article ID 37. doi:10.1186/1029–242X-2012–37 Alber YI: Metric and generalized projection operators in Banach spaces: properties and applications. In Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. Edited by: Kartosator AG. Dekker, New York; 1996:15–50.