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Common Zero for a Finite Family of Monotone Mappings in Hadamard Spaces with Applications

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Abstract

The purpose of this article is to propose a viscosity-type algorithms for solving the common zero for a finite family of monotone mappings in Hadamard spaces. Some applications to convex optimization problem in Hadamard space are also presented.

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References

  1. Martinet, B.: Régularisation \(\prime {d}\)inéquations variationnelles par approximations successives. Rev. Francaise Informat. Recherche. Opèrationnelle. 4, 154–58 (1970)

    MATH  Google Scholar 

  2. Rockafellar, T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877–898 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  3. Güler, O.: On the convergence of the proximal point algorithm for convex minimization. SIAM J. Control Optim. 29, 403–419 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  4. Xu, H.K.: Strong convergence of an iterative method for nonexpansive and accretive operators. J. Math. Anal. Appl. 314, 631–643 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zegeye, H., Shahzad, N.: Strong convergence theorems for a common zero of a finite family of m-accretive mapping. Nonlinear Anal. 66, 1161–1169 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bačâk, M.: The proximal point algorithm in metric spaces. Isr. J. Math. 194, 689–701 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Li, C., López, G., Martín-Márquez, V.: Monotone vector fields and the proximal point algorithm on Hadamard manifolds. J. Lond. Math. Soc. 79, 663–683 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cholamjiak, P.: The modified proximal point algorithm in CAT(0) spaces. Optim. Lett. 9, 1401–1410 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chang, Shih-sen, Yao, Jen-Chih, Wang, Lin, Qin, Li Juan: Some convergence theorems involving proximal point and common fixed points for asymptotically nonexpansive mappings in CAT(0) spaces. Fixed Point Theory Appl. 2016, 68 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chang, Shih-Sen, Wen, Ching-Feng, Yao, Jen-Chih: Proximal point algorithms involving Cesaro type mean of asymptotically nonexpansive mappings in CAT(0) spaces. J. Nonlinear Sci. Appl. 9, 4317–4328 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ranjbar, S., Khatibzadeh, H.: Strong and \(\Delta \)-convergence to a zero of a monotone operator in CAT(0) spaces. Mediterr. J. Math. 14, 56 (2017). (published online March 2, (2017))

    Article  MathSciNet  MATH  Google Scholar 

  12. Khatibzadeh, H., Mohebbi, V., Ranjbar, S.: New results on the proximal point algorithm in nonpositive curvaturemetric spaces. Optimization 66(7), 1191–1199 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, Yuanheng, Li, Yan, Pan, Chanjuan: Strong convergence of a modified viscosity iteration for common zeros of a finite family of accretive mappings. J. Nonlinear Sci. Appl. 10, 4751–4759 (2017)

    Article  MathSciNet  Google Scholar 

  14. Ceng, L.C., Khan, A.R., Ansari, Q.H., Yao, J.C.: Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces. Nonlinear Anal. 70, 1830–1840 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bridson, M.R., Haefliger, A.: Metric Spaces of Non-positive Curvature, Grundlehren der Mathematischen Wissenschaften, vol. 319. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  16. Brown, K.S.: Buildings. Springer, New York (1989)

    Book  MATH  Google Scholar 

  17. Leustean, L.: A quadratic rate of asymptotic regularity for CAT(0)-spaces. J. Math. Anal. Appl. 325, 386–399 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Berg, I.D., Nikolaev, I.G.: Quasilinearization and curvature of Alexandrov spaces. Geom. Dedic. 133, 195–218 (2008)

    Article  MATH  Google Scholar 

  19. Ahmadi Kakavandi, B., Amini, M.: Duality and subdifferential for convex functions on complete CAT(0) metric spaces. Nonlinear Anal. 73, 3450–3455 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lim, T.C.: Remarks on some fixed point theorems. Proc. Am. Math. Soc. 60, 179–182 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ahmadi Kakavandi, B.: Weak topologies in complete CAT(0) metric spaces. Proc. Am. Math. Soc. 141, 1029–1039 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Saejung, S., Yotkaew, P.: Approximation of zeros of inverse strongly monotone operators in Banach spaces. Nonlinear Anal. 75, 742–750 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wangkeeree, R., Preechasilp, P.: Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces, J. Inequal. Appl. 2013 (2013) (Article ID 93)

  24. Chang, Shih-sen, Wang, Lin, Wen, Ching-Feng, Zhang, Jian Qiang: The modified proximal point algorithm in Hadamard spaces. J. Inequal. Appl. 2018, 124 (2018)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The first author was supported by the Natural Science Foundation of China Medical University, Taiwan, and the third author was supported by The Natural Science Foundation Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan.

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Authors and Affiliations

  1. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Shih-sen Chang & Jen-Chih Yao

  2. College of Mathematics, Yibin University, Yibin, 644007, Sichuan, People’s Republic of China

    Shih-sen Chang

  3. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan

    Ching-Feng Wen

  4. School of Science, South West University of Science and Technology, Mianyang, 621010, Sichuan, People’s Republic of China

    Li Yang

  5. Department of Mathematics, Kunming University, Kunming, 650214, Yunnan, People’s Republic of China

    Li-Jian Qin

Authors
  1. Shih-sen Chang
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  2. Jen-Chih Yao
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  3. Ching-Feng Wen
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  4. Li Yang
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  5. Li-Jian Qin
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Correspondence to Shih-sen Chang.

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Chang, Ss., Yao, JC., Wen, CF. et al. Common Zero for a Finite Family of Monotone Mappings in Hadamard Spaces with Applications. Mediterr. J. Math. 15, 160 (2018). https://doi.org/10.1007/s00009-018-1205-x

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  • DOI: https://doi.org/10.1007/s00009-018-1205-x

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