Perturbed approximations of fixed points of nonexpansive mappings in CAT_p(0) spaces

Using the concept of the CATp(0) spaces proposed by Khamsi et al. [Khamsi, M. A. and Shukri, S. A., Generalized CAT(0) spaces. Bull. Belg. Math. Soc. Simon Stevin, 24 (2017), No. 3, 417–426], we establish ∆-convergence and strong convergence of a perturbed variant of Agarwal et al. S-iteration process for nonexpansive mapping. Finally, from them we deduce results valid for α-nonexpansive mappings.

[1]  Jen-Chih Yao,et al.  On modified proximal point algorithms for solving minimization problems and fixed point problems in CAT(κ) spaces , 2019, Mathematical Methods in the Applied Sciences.

[2]  Aurora Fernández-León,et al.  CAT(k)-spaces, weak convergence and fixed points , 2009 .

[3]  Suthep Suantai,et al.  Fixed point theorems for alpha-nonexpansive mappings , 2010, Appl. Math. Lett..

[4]  B. Choi,et al.  THE PROXIMAL POINT ALGORITHM IN UNIFORMLY CONVEX METRIC SPACES , 2016 .

[5]  Assaf Naor,et al.  Poincaré inequalities, embeddings, and wild groups , 2010, Compositio Mathematica.

[6]  David Ariza-Ruiz,et al.  Firmly nonexpansive mappings in classes of geodesic spaces , 2012, 1203.1432.

[7]  William A. Kirk,et al.  A concept of convergence in geodesic spaces , 2008 .

[8]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[9]  Lishan Liu,et al.  Ishikawa and Mann Iterative Process with Errors for Nonlinear Strongly Accretive Mappings in Banach Spaces , 1995 .

[10]  Yuguang Xu,et al.  Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations , 1998 .

[11]  Teck-Cheong Lim.  Fixed point theorems for uniformly Lipschitzian mappings in LP spaces , 1983 .

[12]  Zongben Xu,et al.  Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces , 1991 .

[13]  K. Kuwae.  Resolvent Flows for Convex Functionals and p-Harmonic Maps , 2015 .

[14]  Approximations of Fixed Points in the Hadamard Metric Space CATp(0) , 2019, Mathematics.

[15]  Jürgen Jost,et al.  Convex functionals and generalized harmonic maps into spaces of non positive curvature , 1995 .

[16]  Shin-ichi Ohta,et al.  Convexities of metric spaces , 2007 .

[17]  Hong-Kun Xu.  Inequalities in Banach spaces with applications , 1991 .

[18]  S. Dhompongsa,et al.  On -convergence theorems in CAT(0) spaces , 2008, Comput. Math. Appl..

[19]  Kenyi Calderón,et al.  Hybrid algorithm with perturbations for total asymptotically non-expansive mappings in CAT(0) space , 2019, Int. J. Comput. Math..

[20]  Uwe F. Mayer,et al.  Gradient flows on nonpositively curved metric spaces and harmonic maps , 1998 .

[21]  J. Moreau.  Fonctions convexes duales et points proximaux dans un espace hilbertien , 1962 .

[22]  David Ariza-Ruiz,et al.  The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings , 2014, J. Optim. Theory Appl..

[23]  Fumiaki Kohsaka,et al.  Spherical nonspreadingness of resolvents of convex functions in geodesic spaces , 2016 .

[24]  Liu Qihou,et al.  Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings , 1996 .

[25]  V. Berinde.  Iterative Approximation of Fixed Points , 2007 .