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COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS BY A MODIFIED FASTER ITERATION SCHEME

  • Received : 2009.03.20
  • Accepted : 2010.02.19
  • Published : 2010.09.30

Abstract

We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand, it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme, we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.

Keywords

iteration scheme;nonexpansive self mapping;nonexpansive nonself mapping;rate of convergence;common fixed point;the condition (A');weak and strong convergence

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  2. On an Iterative Process for Generalized Nonexpansive Multi-valued Mappings in Banach Spaces vol.44, pp.4, 2016, https://doi.org/10.1007/s10013-016-0194-y
  3. Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings vol.2012, 2012, https://doi.org/10.1155/2012/817193
  4. Mixed type iterations for multivalued nonexpansive mappings in hyperbolic spaces vol.2014, pp.1, 2014, https://doi.org/10.1186/1687-1812-2014-140
  5. Approximating Fixed Points of Generalized α-Nonexpansive Mappings in Banach Spaces vol.38, pp.2, 2017, https://doi.org/10.1080/01630563.2016.1276075
  6. A Picard-Mann hybrid iterative process vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1812-2013-69
  7. Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces vol.2014, pp.1, 2014, https://doi.org/10.1186/1687-1812-2014-181
  8. A solution of delay differential equations via Picard–Krasnoselskii hybrid iterative process vol.6, pp.1, 2017, https://doi.org/10.1007/s40065-017-0162-8
  9. Common Fixed Points of Two Generalized Asymptotically Quasi-Nonexpansive Mappings vol.0, pp.0, 2015, https://doi.org/10.1515/aicu-2015-0023
  10. Approximating Fixed Points of a General Class of Nonexpansive Mappings in Banach Spaces with Applications vol.74, pp.1, 2019, https://doi.org/10.1007/s00025-018-0930-6
  11. Fixed points of multivalued nonexpansive mappings in Banach spaces vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1812-2012-73

Acknowledgement

Supported by : Kyungnam University Research