Convergence theorem for a finite family of asymptotically demicontractive multi-valued mappings in CAT(0) spaces

References

[1] B. Ahmadi Kakavandi, Weak topologies in complete CAT⁢(0) metric spaces, Proc. Amer. Math. Soc. 141 (2013), no. 3, 1029–1039. 10.1090/S0002-9939-2012-11743-5Search in Google Scholar

[2] K. O. Aremu, C. Izuchukwu, G. C. Ugwunnadi and O. T. Mewomo, On the proximal point algorithm and demimetric mappings in CAT⁢(0) spaces, Demonstr. Math. 51 (2018), no. 1, 277–294. 10.1515/dema-2018-0022Search in Google Scholar

[3] K. O. Aremu, L. O. Jolaoso, C. Izuchukwu and O. T. Mewomo, Approximation of common solution of finite family of monotone inclusion and fixed point problems for demicontractive multivalued mappings in CAT⁢(0) spaces, Ric. Mat. (2019), 10.1007/s11587-019-00446-y. 10.1007/s11587-019-00446-ySearch in Google Scholar

[4] M. Başarır and A. Şahin, On the strong and Δ-convergence of new multi-step and S-iteration processes in a CAT⁢(0) space, J. Inequal. Appl. 2013 (2013), Article ID 482. 10.1186/1029-242X-2013-482Search in Google Scholar

[5] I. D. Berg and I. G. Nikolaev, Quasilinearization and curvature of Aleksandrov spaces, Geom. Dedicata 133 (2008), 195–218. 10.1007/s10711-008-9243-3Search in Google Scholar

[6] M. R. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature, Grundlehren Math. Wiss. 319, Springer, Berlin, 1999. 10.1007/978-3-662-12494-9Search in Google Scholar

[7] F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228. 10.1016/0022-247X(67)90085-6Search in Google Scholar

[8] D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, Grad. Stud. Math. 33, American Mathematical Society, Providence, 2001. 10.1090/gsm/033Search in Google Scholar

[9] S.-S. Chang, L. Wang, H. W. J. Lee and C.-K. Chan, Strong and Δ-convergence for mixed type total asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. 2013 (2013), Article ID 122. 10.1186/1687-1812-2013-122Search in Google Scholar

[10] S. S. Chang, L. Wang, H. W. J. Lee, C.-K. Chan and L. Yang, Demiclosed principle and Δ-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Appl. Math. Comput. 219 (2012), no. 5, 2611–2617. 10.1016/j.amc.2012.08.095Search in Google Scholar

[11] H. Dehghan, C. Izuchukwu, O. T. Mewomo, D. A. Taba and G. C. Ugwunnadi, Iterative algorithm for a family of monotone inclusion problems in CAT⁢(0) spaces, Quaest. Math. (2019), 10.2989/16073606.20. 10.2989/16073606.20Search in Google Scholar

[12] H. Dehghan and J. Rooin, Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces, preprint (2014), https://arxiv.org/abs/1410.1137v1. Search in Google Scholar

[13] S. Dhompongsa, W. A. Kirk and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8 (2007), no. 1, 35–45. Search in Google Scholar

[14] S. Dhompongsa, W. A. Kirk and B. Sims, Fixed points of uniformly Lipschitzian mappings, Nonlinear Anal. 65 (2006), no. 4, 762–772. 10.1016/j.na.2005.09.044Search in Google Scholar

[15] S. Dhompongsa and B. Panyanak, On Δ-convergence theorems in CAT⁢(0) spaces, Comput. Math. Appl. 56 (2008), no. 10, 2572–2579. 10.1016/j.camwa.2008.05.036Search in Google Scholar

[16] N. Hussain and M. A. Khamsi, On asymptotic pointwise contractions in metric spaces, Nonlinear Anal. 71 (2009), no. 10, 4423–4429. 10.1016/j.na.2009.02.126Search in Google Scholar

[17] F. O. Isiogugu, Demiclosedness principle and approximation theorems for certain classes of multivalued mappings in Hilbert spaces, Fixed Point Theory Appl. 2013 (2013), Article ID 61. 10.1186/1687-1812-2013-61Search in Google Scholar

[18] C. Izuchukwu, H. A. Abass and O. T. Mewomo, Viscosity approximation method for solving minimization problem and fixed point problem for nonexpansive multivalued mapping in CAT⁢(0) spaces, Ann. Acad. Rom. Sci. Ser. Math. Appl. 11 (2019), no. 1, 130–157. Search in Google Scholar

[19] C. Izuchukwu, K. O. Aremu, A. A. Mebawondu and O. T. Mewomo, A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space, Appl. Gen. Topol. 20 (2019), no. 1, 193–210. 10.4995/agt.2019.10635Search in Google Scholar

[20] C. Izuchukwu, A. A. Mebawondu, K. O. Aremu, H. A. Abass and O. T. Mewomo, Viscosity iterative techniques for approximating a common zero of monotone operators in a Hadamard space, Rend. Circ. Mat. Palermo (2) (2019), 10.1007/s12215-019-00415-2. 10.1007/s12215-019-00415-2Search in Google Scholar

[21] W. A. Kirk, Geodesic geometry and fixed point theory, Seminar of Mathematical Analysis (Malaga/Seville 2002/2003), Colecc. Abierta 64, Universidad de Sevilla, Seville (2003), 195–225. Search in Google Scholar

[22] W. A. Kirk, Fixed point theorems in CAT⁢(0) spaces and ℝ-trees, Fixed Point Theory Appl. 2004 (2004), no. 4, 309–316. 10.1155/S1687182004406081Search in Google Scholar

[23] W. A. Kirk, Geodesic geometry and fixed point theory. II, International Conference on Fixed Point Theory and Applications, Yokohama Publishers, Yokohama (2004), 113–142. 10.1155/S1687182004406081Search in Google Scholar

[24] W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), no. 12, 3689–3696. 10.1016/j.na.2007.04.011Search in Google Scholar

[25] X.-D. Liu and S.-s. Chang, Convergence theorems on total asymptotically demicontractive and hemicontractive mappings in CAT(0) spaces, J. Inequal. Appl. 2014 (2014), Article ID 436. 10.1186/1029-242X-2014-436Search in Google Scholar

[26] P.-E. Maingé, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal. 16 (2008), no. 7–8, 899–912. 10.1007/s11228-008-0102-zSearch in Google Scholar

[27] S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475–488. 10.2140/pjm.1969.30.475Search in Google Scholar

[28] B. Nanjaras and B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT⁢(0) spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 268780. 10.1155/2010/268780Search in Google Scholar

[29] N. Shahzad and H. Zegeye, Strong convergence results for nonself multimaps in Banach spaces, Proc. Amer. Math. Soc. 136 (2008), no. 2, 539–548. 10.1090/S0002-9939-07-08884-3Search in Google Scholar

[30] W. Takahashi, A convexity in metric space and nonexpansive mappings. I, Kodai Math. Sem. Rep. 22 (1970), 142–149. 10.2996/kmj/1138846111Search in Google Scholar

[31] G. C. Ugwunnadi, C. Izuchukwu and O. T. Mewomo, On nonspreading-type mappings in Hadamard spaces, Bol. Soc. Parana. Mat. (3) (2018), 10.5269/bspm.41768. 10.5269/bspm.41768Search in Google Scholar

[32] G. C. Ugwunnadi, C. Izuchukwu and O. T. Mewomo, Strong convergence theorem for monotone inclusion problem in CAT⁢(0) spaces, Afr. Mat. 30 (2019), no. 1–2, 151–169. 10.1007/s13370-018-0633-xSearch in Google Scholar

[33] H.-K. Xu, Iterative algorithms for nonlinear operators, J. Lond. Math. Soc. (2) 66 (2002), no. 1, 240–256. 10.1112/S0024610702003332Search in Google Scholar