Fixed points of generalized hybrid mappings in 2-uniformly convex hyperbolic metric spaces

Abstract

Keywords: Hybrid Mapping; Fixed Point; Hyperbolic Metric Spaces

References

1. Takahashi, W. Introduction to nonlinear and convex analysis. Yokohama, Japan: Yokohama Publishers,  (α − 2α 2 ) 2  α d 2 (T (0, α1 ) , (0, α 2 )) = d 2   0, 1  , (0, α 2 ) = 1 2009.  2   4 [2] Kohsaka, F, Takahashi, W. Fixed point theorems for d 2 (T (0, α 2 ) , (0, α1 )) = (α 2 − 2α1 ) 2 a class of nonlinear mappings related to maximal 4 monotone operators in Banach spaces. Archiv der α Mathematik 2008;91:166−177. [CrossRef]  α 2  d 2 (T (0, α1 ) , (0, α1 )) = d 2  0, 1 , (0, α1 ) = 1  
2. Kawasaki T, Takahashi W. Existence and mean 0 Then we have (0, 0) = (0, α) Î C and T ( 0 ,0 ) =  0 ,  = ( 0 ,0 ) . approximation of fixed points of generalized hybrid  2 mappings in Hilbert spaces. J Nonlinear Convex Anal 2013;14:71−87. CONCLUSION [7] Hojo M, Suzuki T, Takahashi W. Fixed point We introduce generalized hybrid mappings in hyperbolic theorems and convergence theorems for general- metric spaces. We first show that the set of fixed points of ized hybrid non-self mappings in Hilbert spaces. such mappings is closed and convex. We then prove the exis- J Nonlinear Convex Anal 2013;14:363−376. [CrossRef] tence of fixed point of these mappings and finally approxi-
3. Lin LJ, Chuang CS, Yu ZT. Fixed point theo- mate the fixed point using Mann iterative process. We have rems and del-convergence theorems for general- also provided an example of generalized hybrid mappings in ized hybrid mappings on CAT (0) spaces. Fixed the setting of -trees for the first time in the literature. Point Theory and Algorithms for Sciences and Engineering 2011;2011:49. [CrossRef] AUTHORSHIP CONTRIBUTIONS [9] Dehaish BI, Khamsi MA, Khan AR. Mann itera- tion process for asymptotic pointwise nonexpan- Authors equally contributed to this work. sive mappings in metric spaces. J Math Anal Appl 2013;397:861−868. [CrossRef] DATA AVAILABILITY STATEMENT
4. Menger K. Untersuchungen über allgemeine The authors confirm that the data that supports the Metrik. Mathematische Annalen 1928;100:75−163. findings of this study are available within the article. Raw (Deutsch) [CrossRef] 234 Sigma J Eng Nat Sci, Vol. 40, No. 2, pp. 227–234, June, 2022
5. Khamsi MA, Khan AR. Inequalities in metric spaces [13] Reich S, Shafrir I. Nonexpansive iterations in hyper- with applications. Nonlinear Anal Theory Methods bolic spaces. Nonlinear Anal Theory Methods Appl Appl 2011;74:4036−4045. [CrossRef] 1990;15:537−558. [CrossRef]
6. Xu HK. Inequalities in Banach spaces with appli- [14] Kirk W. A. Some recent results in metric fixed point cations. Nonlinear Anal Theory Methods Appl theory. J Fixed Point Theory Appl 2007;2:195−207. 1991;16:1127−1138. [CrossRef] [CrossRef]

Share and Cite