Iterative algorithms for infinite accretive mappings and applications to p-Laplacian-like differential systems

详细信息    查看全文

• 作者：Li Wei ; Ravi P Agarwal
• 关键词：47H05 ; 47H09 ; 47H10 ; accretive mapping ; gauge function ; contraction ; common zero point ; retraction ; p ; Laplacian ; like differential systems
• 刊名：Fixed Point Theory and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,772 KB
• 参考文献：1. Barbu, V: Nonlinear Semigroups and Differential Equations in Banach Space. Noordhoff, Leyden (1976) CrossRef
  2. Agarwal, RP, O’Regan, D, Sahu, DR: Fixed Point Theory for Lipschitz-Type Mappings with Applications. Springer, Berlin (2008)
  3. Browder, FE: Convergence theorems for sequences of nonlinear operators in Banach spaces. Math. Z. 100(3), 201-225 (1967) MathSciNet CrossRef MATH
  4. Takahashi, W: Proximal point algorithms and four resolvents of nonlinear operators of monotone type in Banach spaces. Taiwan. J. Math. 12(8), 1883-1910 (2008) MATH
  5. Shehu, Y, Ezeora, JN: Path convergence and approximation of common zeroes of a finite family of m-accretive mappings in Banach spaces. Abstr. Appl. Anal. 2010, Article ID 285376 (2010) MathSciNet
  6. Takahashi, W: Nonlinear Functional Analysis: Fixed Point Theory and Its Application. Yokohama Publishers, Yokohama (2000)
  7. Rockafellar, RT: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14(5), 877-898 (1976) MathSciNet CrossRef MATH
  8. Petrusel, A, Yao, JC: Viscosity approximation by generalized contractions for resolvents of accretive operators in Banach spaces. Acta Math. Sin. 25(4), 553-564 (2009) MathSciNet CrossRef MATH
  9. Qin, XL, Su, YF: Approximation of a zero point of accretive operator in Banach spaces. J. Math. Anal. Appl. 329, 415-424 (2007) MathSciNet CrossRef MATH
  10. Ceng, LC, Ansari, QH, Schaible, S, Yao, JC: Hybrid viscosity approximation method for zeros of m-accretive operators in Banach spaces. Numer. Funct. Anal. Optim. 32(11), 1127-1150 (2011) MathSciNet CrossRef
  11. Ceng, LC, Schaible, S, Yao, JC: Hybrid steepest decent methods for zeros of nonlinear operators with applications to variational inequalities. J. Optim. Theory Appl. 141, 75-91 (2009) MathSciNet CrossRef
  12. Ceng, LC, Wu, SY, Yao, JC: New accuracy criteria for modified approximate proximal point algorithms in Hilbert spaces. Taiwan. J. Math. 12(7), 1691-1705 (2008) MathSciNet MATH
  13. Xu, HK: Strong convergence of an iterative method for nonexpansive and accretive operators. J. Math. Anal. Appl. 314, 631-643 (2006) MathSciNet CrossRef MATH
  14. Cho, JC, Kang, SM, Zhou, HY: Approximate proximal point algorithms for finding zeroes of maximal monotone operator in Hilbert spaces. J. Inequal. Appl. 2008, Article ID 598191 (2008) MathSciNet
  15. Ceng, LC, Khan, AR, Ansari, QH, Yao, JC: Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces. Nonlinear Anal. 70, 1830-1840 (2009) MathSciNet CrossRef MATH
  16. Halpern, B: Fixed points of nonexpansive maps. Bull. Am. Math. Soc. 73, 957-961 (1967) CrossRef MATH
  17. Zegeye, H, Shahzad, N: Strong convergence theorems for a common zero of a finite family of m-accretive mappings. Nonlinear Anal. 66, 1161-1169 (2007) MathSciNet CrossRef MATH
  18. Hu, LY, Liu, LW: A new iterative algorithm for common solutions of a finite family of accretive operators. Nonlinear Anal. 70, 2344-2351 (2009) MathSciNet CrossRef MATH
  19. Yao, Y, Liou, YC, Marino, G: Strong convergence of two iterative algorithms for nonexpansive mappings in Hilbert spaces. Fixed Point Theory Appl. 2009, Article ID 279058 (2009) MathSciNet
  20. Wei, L, Tan, RL: Iterative scheme with errors for common zeros of finite accretive mappings and nonlinear elliptic systems. Abstr. Appl. Anal. 2014, Article ID 646843 (2014) MathSciNet
  21. Wang, SH, Zhang, P: Some results on an infinite family of accretive operators in a reflexive Banach space. Fixed Point Theory Appl. 2015, Article ID 8 (2015) CrossRef
  22. Bruck, RE: Properties of fixed-point sets of nonexpansive mappings in Banach spaces. Trans. Am. Math. Soc. 179, 251-262 (1973) MathSciNet CrossRef MATH
  23. Lim, TC: Fixed point theorems for asymptotically nonexpansive mapping. Nonlinear Anal. 22, 1345-1355 (1994) MathSciNet CrossRef MATH
  24. Liu, LS: Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces. J. Math. Anal. Appl. 194, 114-125 (1995) MathSciNet CrossRef MATH
  25. Browder, FE: Nonexpansive nonlinear operators in a Banach space. Proc. Natl. Acad. Sci. USA 54, 1041-1044 (1965) MathSciNet CrossRef MATH
  26. Wei, L, Agarwal, RP: Existence of solutions to nonlinear Neumann boundary value problems with generalized p-Laplacian operator. Comput. Math. Appl. 56, 530-541 (2008) MathSciNet CrossRef MATH
  27. Calvert, BD, Gupta, CP: Nonlinear elliptic boundary value problems in \(L^{p}\) -spaces and sums of ranges of accretive operators. Nonlinear Anal. 2, 1-26 (1978) MathSciNet CrossRef MATH
  28. Pascali, R, Sburlan, S: Nonlinear Mappings of Monotone Type. Editura Academiei, Bucharest (1978) CrossRef MATH
  29. Wei, L, Agarwal, RP, Wong, PJY: Results on the existence of solution of p-Laplacian-like equation. Adv. Math. Sci. Appl. 23(1), 153-167 (2013) MathSciNet MATH
  30. Li, LK, Guo, YT: The Theory of Sobolev Space. Shanghai Science and Technology Press, Shanghai (1981) (in Chinese)
  31. Wei, L, He, Z: The applications of sums of ranges of accretive operators to nonlinear equations involving the p-Laplacian operator. Nonlinear Anal. 24, 185-193 (1995) MathSciNet CrossRef MATH
  
• 作者单位：Li Wei (1)
  Ravi P Agarwal (2) (3)
  
  1. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061, China
  2. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, 78363, USA
  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
  
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

Some new iterative algorithms with errors for approximating common zero point of an infinite family of m-accretive mappings in a real Banach space are presented. A path convergence theorem and some new weak and strong convergence theorems are proved by means of some new techniques, which extend the corresponding works by some authors. As applications, an infinite p-Laplacian-like differential system is investigated, from which we construct an infinite family of m-accretive mappings and discuss the connections between the equilibrium solution of the differential systems and the zero point of the m-accretive mappings. Keywords accretive mapping gauge function contraction common zero point retraction p-Laplacian-like differential systems