Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 69, 2020 - Issue 4
147
Views
5
CrossRef citations to date
0
Altmetric
Articles

Convergence analysis and stability of perturbed three-step iterative algorithm for generalized mixed ordered quasi-variational inclusion involving XOR operator

, , &
Pages 821-845 | Received 08 Mar 2018, Accepted 22 Jul 2019, Published online: 16 Aug 2019

References

  • Amann H. On the number of solutions of nonlinear equations in ordered Banach spaces. J Funct Anal. 1972;11(3):346–384. doi: 10.1016/0022-1236(72)90074-2
  • Ahmad I, Pang CT, Ahmad R, et al. System of Yosida inclusions involving XOR operator. J Nonlinear Convex Anal. 2017;18(5):831–845.
  • Fang YP, Huang NJ. H-monotone operator and resolvent operator technique for variational inclusions. Appl Math Comput. 2003;145(2–3):795–803.
  • Fang YP, Huang NJ. H-accretive operator and resolvent operator technique for variational inclusions in Banach spaces. Appl Math Lett. 2004;17(6):647–653. doi: 10.1016/S0893-9659(04)90099-7
  • Noor MA. New approximation schemes for general variational inequalities. J Math Anal Appl. 2000;251:217–229. doi: 10.1006/jmaa.2000.7042
  • Noor MA. A predictor-corrector algorithm for general variational inequalities. Appl Math Lett. 2001;14:53–58. doi: 10.1016/S0893-9659(00)00112-9
  • Schaefer HH. Banach lattices and positive operators. Berlin: Springer; 1974. doi:10.1007/978-3-642-65970-6.
  • Fang YP, Huang NJ. Approximate solutions for non-linear variational inclusions with (H,η)-monotone operator, Sichuan University; 2003. (Research Report).
  • Noor MA. Three-step iterative algorithms for multivalued quasi-variational inclusions. J Math Anal Appl. 2001;255:589–604. doi: 10.1006/jmaa.2000.7298
  • Li HG. Approximation solution for general nonlinear ordered variational inequalities and ordered equations in ordered Banach space. Nonlinear Anal Forum. 2008;13(2):205–214.
  • Li HG. Approximation solution for a new class general nonlinear ordered variational inequalities and ordered equations in ordered Banach space. Nonlinear Anal Forum. 2009;14:89–97.
  • Li HG, Qiu D, Zou Y. Characterizations of weak-ANODD set-valued mappings with applications to approximate solution of GNMOQV inclusions involving ⊕ operator in ordered Banach spaces. Fixed Point Theory Appl. 2013. doi: 10.1186/1687-1812-2013-241.
  • Li HG, Pan XB, Deng ZY, et al. Solving GNOVI frameworks involving (γG,λ)-weak-GRD set-valued mappings in positive Hilbert spaces. Fixed Point Theory Appl. 2014;2014:146. doi: 10.1186/1687-1812-2014-146
  • Li HG, Yang Y, Jin MM, et al. Stability for a new class of GNOVI with (γG,λ)-weak-GRD mapping in positive Hilbert spaces. Math Probl Eng. 2016;2016:7. Article ID 9217091.
  • Ahmad I, Ahmad R, Iqbal J. A resolvent approach for solving a set-valued variational inclusion problem using weak-RRD set-valued mapping. Korean J Math. 2016;24(2):199–213. doi: 10.11568/kjm.2016.24.2.199
  • Glowinski G, Tallec PL. Augmented Lagrangian and operator splitting methods in nonlinear mechanics. Philadelphia: SIAM; 1989.
  • Li HG. A nonlinear inclusion problem involving (α,λ)-NODM set-valued mappings in ordered Hilbert space. Appl Math Lett. 2012;25:1384–1388. doi: 10.1016/j.aml.2011.12.007
  • Du YH. Fixed points of increasing operators in ordered Banach spaces and applications. Appl Anal. 1990;38:1–20. doi: 10.1080/00036819008839957
  • Osilike MO. Stability results for the Ishikawa fixed point iteration procedure. Ind J Pure Appl Math. 1995;26(10):937–945.
  • Weng XL. Fixed point iteration for local strictly pseudocontractive mapping. Proc A.M.S. 1991;113(3):727–731. doi: 10.1090/S0002-9939-1991-1086345-8

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.