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Year 2018, Volume: 1 Issue: 2, 1 - 5, 01.06.2018

Abstract

References

  • W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai. Math. Sem.Rep. 22 (1970) 142-149.
  • Y. X. Tian, Convergence of an Ishikawa type iterative scheme for asymptotically quasi- nonexpansive mappings, Comput. Math. Appl. 49 (2005) 1905-1912.
  • C. Wang, L. W. Liu, Convergence theorems for fixed points of uniformly uniformly quasi- Lipschitzian mappings in convex metric spaces, Nonlinear Anal. TMA 70 (2009) 2067-2091.
  • S.S. Chang, L. Yang, X. R. Wang, Stronger convergence theorems for an infinite family of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comp. 217 (2010) 277-282.
  • Q. Y. Liu, Z. B. Liu, N. J. Huang, Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comp. 216 (2010) 883-889.
  • B. S. Lee, Strong convergence theorems with a Noor-type iterative scheme in convex metric spaces, Com. Math. Appl. 61 (2011) 3218-3225.
  • Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with errors number, J. Math. Anal. Appl. 259 (2001) 18-24.
  • S. H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory and Applications, Open acces, doi:10.1186/1687-1812-2013, 69.
  • L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476.
  • S. Elmas and M. Ozdemir, Convergence of a general iterative scheme for three families of uniformly quasi-Lipschitzian mappings in convex metric spaces, Advances in Fixed Point Theory 3 (2013) 406-417.

CONVERGENCE OF THE PICARD-MANN HYBRID ITERATION IN CONVEX CONE METRIC SPACES

Year 2018, Volume: 1 Issue: 2, 1 - 5, 01.06.2018

Abstract

In this study we try to show convergence of the Picard-Mann hybrid Iteration in convex cone metric spaces for common fixed points of infinite families of uniformly quasi-Lipschitzian mappings and quasi-nonexpansive mappings. A convex cone mtric space is a cone metric space with a convex structure

References

  • W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai. Math. Sem.Rep. 22 (1970) 142-149.
  • Y. X. Tian, Convergence of an Ishikawa type iterative scheme for asymptotically quasi- nonexpansive mappings, Comput. Math. Appl. 49 (2005) 1905-1912.
  • C. Wang, L. W. Liu, Convergence theorems for fixed points of uniformly uniformly quasi- Lipschitzian mappings in convex metric spaces, Nonlinear Anal. TMA 70 (2009) 2067-2091.
  • S.S. Chang, L. Yang, X. R. Wang, Stronger convergence theorems for an infinite family of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comp. 217 (2010) 277-282.
  • Q. Y. Liu, Z. B. Liu, N. J. Huang, Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comp. 216 (2010) 883-889.
  • B. S. Lee, Strong convergence theorems with a Noor-type iterative scheme in convex metric spaces, Com. Math. Appl. 61 (2011) 3218-3225.
  • Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with errors number, J. Math. Anal. Appl. 259 (2001) 18-24.
  • S. H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory and Applications, Open acces, doi:10.1186/1687-1812-2013, 69.
  • L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476.
  • S. Elmas and M. Ozdemir, Convergence of a general iterative scheme for three families of uniformly quasi-Lipschitzian mappings in convex metric spaces, Advances in Fixed Point Theory 3 (2013) 406-417.
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Details

Primary Language English
Journal Section Some Notes on the Extendibility of an Especial Family of Diophantine 𝑷𝟐 Pairs
Authors

Süheyla Elmas This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

APA Elmas, S. (2018). CONVERGENCE OF THE PICARD-MANN HYBRID ITERATION IN CONVEX CONE METRIC SPACES. Journal of Advanced Mathematics and Mathematics Education, 1(2), 1-5.