Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces

Authors

  • Isa Yildirim Department of Mathematics, Faculty of Science, Ataturk University, 25240, Turkey
  • Murat Özdemir Department of Mathematics, Faculty of Science, Ataturk University, 25240, Turkey

DOI:

https://doi.org/10.5556/j.tkjm.42.2011.511

Keywords:

Asymptotically quasi-nonexpansive mapping, Common fixed point, Weak and strong convergence theorems

Abstract

In this paper, we consider a composite iterative algorithm for approximating common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

References

S. S. Chang, Y. J. Cho and S.M. Kang,NonlinearOperator Theory in ProbabilisticMetric Spaces, Nova Science Publishers, Huntington,USA, 2001.

G. Jungck, Compatible mappings and common fixed pointsZ, Internat. J. Math. & Math. Sci., 9 (1986), 771–

G. Jungck and B.E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227–238.

K.Menger, Statistical metric, Proc. Nat. Acad. (USA) 28 (1942), 535–537.

S. N. Mishra, Common fixed points of compatible mappings in probabilistic metric spaces, Math. Japon., 36

(1991), 283–289.

D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput., 195

(2008), 86–93.

B. D. Pant and S. Chauhan, A contraction theoreminMenger space using weak compatibility, Int. J.Math. Sci.& Engg. Appls., 4 (2010), 177–186.

B. Schweizer and A. Sklar, Statisticalmetric spaces, Pacific J.Math., 10 (1960), 313–334.

B. Schweizer and A. Sklar, ProbabilisticMetric Spaces, Elsevier, North-Holland,New York, 1983.

V. M. Sehgal and A. T. Bharucha-Reid, Fixed point of contraction mappings on probabilistic metric spaces, Math. SystemTheory, 6 (1972), 97–102.

S. Shakeri, A contraction theoreminMenger probabilisticmetric spaces, J. Nonlinear Sci. Appl., 1(2008), 189–193.

B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl., 301 (2005), 439–448.

Downloads

Published

2010-12-22

How to Cite

Yildirim, I., & Özdemir, M. (2010). Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces. Tamkang Journal of Mathematics, 42(1), 19–30. https://doi.org/10.5556/j.tkjm.42.2011.511

Issue

Section

Papers