Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces
We define SP-iteration procedure associated with three selfmaps T1, T2, T3 defined on a nonempty convex subset of a convex metric space X and prove ∆-convergence of this iteration procedure to a common fixed point of T1, T2, T3 under the hypotheses that each Ti is either an α-nonexpansive map or a...
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| Format: | Article |
| Language: | English |
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ATNAA
2020-06-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
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| Online Access: | http://static.dergipark.org.tr/article-download/c545/45af/5485/5ea4b124bf13c.pdf? |
| _version_ | 1797906476836061184 |
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| author | Venkata Ravindranadh Babu Gutti , Satyanarayana Gedala |
| author_facet | Venkata Ravindranadh Babu Gutti , Satyanarayana Gedala |
| author_sort | Venkata Ravindranadh Babu Gutti , Satyanarayana Gedala |
| collection | DOAJ |
| description | We define SP-iteration procedure associated with three selfmaps T1, T2, T3 defined on a nonempty convex
subset of a convex metric space X and prove ∆-convergence of this iteration procedure to a common fixed point of T1, T2, T3 under the hypotheses that each Ti is either an α-nonexpansive map or a Suzuki nonexpansive map in the setting of uniformly convex metric spaces. Also, we prove the strong convergence of this iteration procedure to a common fixed point of T1, T2, T3 under certain additional hypotheses namely either
semi-compact or condition (D). |
| first_indexed | 2024-04-10T10:21:31Z |
| format | Article |
| id | doaj.art-c7a61a6652d14484a5382a6403791d5a |
| institution | Directory Open Access Journal |
| issn | 2587-2648 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T10:21:31Z |
| publishDate | 2020-06-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-c7a61a6652d14484a5382a6403791d5a2023-02-15T16:21:35ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482587-26482020-06-014211212010.31197/atnaa.649269Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spacesVenkata Ravindranadh Babu Gutti , Satyanarayana GedalaWe define SP-iteration procedure associated with three selfmaps T1, T2, T3 defined on a nonempty convex subset of a convex metric space X and prove ∆-convergence of this iteration procedure to a common fixed point of T1, T2, T3 under the hypotheses that each Ti is either an α-nonexpansive map or a Suzuki nonexpansive map in the setting of uniformly convex metric spaces. Also, we prove the strong convergence of this iteration procedure to a common fixed point of T1, T2, T3 under certain additional hypotheses namely either semi-compact or condition (D).http://static.dergipark.org.tr/article-download/c545/45af/5485/5ea4b124bf13c.pdf?sp-iteration procedureα-nonexpansive mapsuzuki nonexpansive mapcommon fixed point∆-convergencestrong convergenceuniformly convex metric space |
| spellingShingle | Venkata Ravindranadh Babu Gutti , Satyanarayana Gedala Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces Advances in the Theory of Nonlinear Analysis and its Applications sp-iteration procedure α-nonexpansive map suzuki nonexpansive map common fixed point ∆-convergence strong convergence uniformly convex metric space |
| title | Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces |
| title_full | Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces |
| title_fullStr | Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces |
| title_full_unstemmed | Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces |
| title_short | Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces |
| title_sort | iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces |
| topic | sp-iteration procedure α-nonexpansive map suzuki nonexpansive map common fixed point ∆-convergence strong convergence uniformly convex metric space |
| url | http://static.dergipark.org.tr/article-download/c545/45af/5485/5ea4b124bf13c.pdf? |
| work_keys_str_mv | AT venkataravindranadhbabuguttisatyanarayanagedala iterativeapproximationofcommonfixedpointsofgeneralizednonexpansivemapsinconvexmetricspaces |