Iterative approximation of fixed points of a general class of non-expansive mappings in hyperbolic metric spaces. (English) Zbl 1491.47077
Summary: In this article, we enquire for a couple of weak and strong convergence results involving generalized \(\alpha \)-Reich-Suzuki non-expansive mappings in the setting of a hyperbolic metric space. Particularly, we make use of the recently proposed JF-iteration scheme to attain our theories and further, we attest that this algorithm has a faster convergence rate than that of \(M^*\) iteration. Additionally, we explore several interesting properties related to the fixed point set of such mappings and approximate fixed point sequences also. Eventually, we furnish pertinent examples to substantiate our attained findings and compare the newly proposed scheme with that of some other well-known algorithms using MATLAB 2017a software.
MSC:
| 47J26 | Fixed-point iterations |
| 47H20 | Semigroups of nonlinear operators |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
Keywords:
non-expansive mappings; hyperbolic metric spaces; iterative algorithms; demiclosedness; weak convergence; strong convergence; \(\Delta\)-convergence; condition (\(I\))Software:
MatlabReferences:
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