The Modified Multi-step Iteration Process for Pairwise Generalized Nonexpansive Mappings in CAT(0) Spaces

1. Abbas, M., Nazir, T.: A new faster iteration process applied to constrained minimization and feasibility problems. Mat. Vesnik 66(2), 223–234 (2014)

   MathSciNet  MATH  Google Scholar 

2. Agarwal, R.P., O’Regan, D., Sahu, D.R.: Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. 8(1), 61–79 (2007)

   MathSciNet  MATH  Google Scholar 

3. Borisenko, A.A., Gallego, E., Reventós, A.: Relation between area and volume for \(\lambda \)-convex sets in Hadamard manifolds. Differential Geom. Appl. 14(3), 267–280 (2001)

   Article  MathSciNet  MATH  Google Scholar 

4. Bridson, M.R., Haefliger, A.: Metric spaces of non-positive curvature. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319. Springer, Heidelberg (1999)

   MATH  Google Scholar 

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

   Book  MATH  Google Scholar 

6. Bruhat, F., Tits, J.: Groupes réductifs sur un corps local. Inst. Hautes Études Sci. Publ. Math. 41, 5–251 (1972)

   Article  MATH  Google Scholar 

7. Chang, S.S., Wang, L., Lee, H.W.J., Chan, C.K., Yang, L.: Demiclosed principle and \(\varDelta \)-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces. Appl. Math. Comput. 219(5), 2611–2617 (2012)

   MathSciNet  MATH  Google Scholar 

8. Dhompongsa, S., Kirk, W.A., Sims, B.: Fixed points of uniformly Lipschitzian mappings. Nonlinear Anal. 65(4), 762–772 (2006)

   Article  MathSciNet  MATH  Google Scholar 

9. Dhompongsa, S., Panyanak, B.: On \(\varDelta \)-convergence theorems in CAT(0) spaces. Comput. Math. Appl. 56(10), 2572–2579 (2008)

   Article  MathSciNet  MATH  Google Scholar 

10. García Falset, J., Llorens-Fuster, E., Suzuki, T.: Fixed point theory for a class of generalized nonexpansive mappings. J. Math. Anal. Appl. 375(1), 185–195 (2011)

    Article  MathSciNet  MATH  Google Scholar 

11. Goebel, K., Reich, S.: Uniform convexity, hyperbolic geometry, and nonexpansive mappings. Monographs and Textbooks in Pure and Applied Mathematics, vol. 83. Marcel Dekker Inc., New York (1984)

    MATH  Google Scholar 

12. Ishikawa, S.: Fixed points by a new iteration method. Proc. Amer. Math. Soc. 44, 147–150 (1974)

    Article  MathSciNet  MATH  Google Scholar 

13. Kirk, W.A.: Fixed point theorems in CAT(0) spaces and R-trees. Fixed Point Theor. Appl. 2004(4), 309–316 (2004)

    Article  MathSciNet  MATH  Google Scholar 

14. Kirk, W.A., Panyanak, B.: A concept of convergence in geodesic spaces. Nonlinear Anal. 68(12), 3689–3696 (2008)

    Article  MathSciNet  MATH  Google Scholar 

15. Lim, T.C.: Remarks on some fixed point theorems. Proc. Amer. Math. Soc. 60, 179–182 (1977). 1976

    Article  MathSciNet  MATH  Google Scholar 

16. Mann, W.R.: Mean value methods in iteration. Proc. Amer. Math. Soc. 4, 506–510 (1953)

    Article  MathSciNet  MATH  Google Scholar 

17. Noor, M.A.: New approximation schemes for general variational inequalities. J. Math. Anal. Appl. 251(1), 217–229 (2000)

    Article  MathSciNet  MATH  Google Scholar 

18. Pakkaranang, N., Ngiamsunthorn, P.S., Kumam, P., Cho, Y.J.: Convergence theorems of the modified S-type iterative method for (\(\alpha, \beta \))-generalized hybrid mappings in CAT(0) spaces. J. Math. Anal. 8(1), 103–112 (2017)

    MathSciNet  Google Scholar 

19. Senter, H.F., Dotson Jr., W.G.: Approximating fixed points of nonexpansive mappings. Proc. Amer. Math. Soc. 44, 375–380 (1974)

    Article  MathSciNet  MATH  Google Scholar 

20. Suzuki, T.: Fixed point theorems and convergence theorems for some generalized nonexpansive mappings. J. Math. Anal. Appl. 340(2), 1088–1095 (2008)

    Article  MathSciNet  MATH  Google Scholar 

21. Thakur, B.S., Thakur, D., Postolache, M.: A new iteration scheme for approximating fixed points of nonexpansive mappings. Filomat 30(10), 2711–2720 (2016)

    Article  MathSciNet  MATH  Google Scholar 

22. Zhang, S., Zhou, J., Ciu, Y.: Common fixed point properties for pairwise generalized nonexpansive type mappings in geodesic spaces. J. Nonlinear Sci. Appl. (preprint)

    Google Scholar 

Download references