International Journal of Nonlinear Analysis and Applications

Stability and convergence theorems of pointwise asymptotically nonexpansive random operator in Banach space

Document Type : Research Paper

Author

Department of mathematics, college of Education for pure science (Ibn- AL-Haitham), university of Baghdad, Iraq.

Abstract

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

Keywords

[1] O. Hanš, Reduzierende zufällige transformationen, Czechoslov. Math. J. 7(1) (1975), 154–158.
[2] A. Špaček, Zufällige gleichungen, Czechoslov, Math. J. 5(4) (1955) 462–466.
[3] S. Itoh, A random fixed point theorem for a multivalued contraction mapping, Pacific J. Math. 68(1) (1977) 85–90.
[4] S. Itoh, Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67(2) (1979) 261–273.
[5] V. M. Sehgal and S. P. Singh, On random approximations and a random fixed point theorem for set-valued mappings, Proc. Am. Math. Soc. 95(1) (1985) 91–94.
[6] N. S. Papageorgiou, Random fixed point theorems for measurable multifunctions in Banach spaces, Proc. Am. Math. Soc., 97(3) (1986) 507–514.
[7] T.C. Lin, Random approximations and random fixed point theorems for non-self-maps, Proc. Am. Math. Soc. 103(4) (1988) 1129–1135.
[8] O. Hans, Random fixed point theorems, in Transactions of the first Prague Conference on Information Theory, Statistical Decision Functions, Random Process, (1957) 105–125.
[9] O. Hans, Random operator equations, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 2 (1961),
[10] I. Beg and N. Shahzad, Random fixed point theorems on product spaces, Int. J. Stoch. Anal. 6(2) (1993) 95–106.
[11] I. Beg and N. Shahzad, Common Random fixed points of random multivalued operators on metric spaces, Boll. UMI 7 9-A) (1995) 493–503.
[12] N. Shahzad, Random fixed point and approximations, Quaid-i-Azam University Islamabad, Pakistan, 1995.
[13] R.A. Rashwan, H. A. Hammad, Random common fixed point theorem for random weakly subsequentially continuous generalized contractions with application, Int. J. Pure Appl. Math. 109(4) (2016) 813–826.
[14] Z. Opial, Weak convergence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967) 531–537.
[15] B.D. Karande and S. G. Shete, Existence and Attractivity Results for Volterra Type Nonlinear Perturbed Random Integral Equations, J. Comput. Math. Sci. 7(8) (2016) 398–407.
[16] G.A. Okeke, J. K. Kim, Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process, J. Inequalities Appl. 2015(1) (2015) 290.
[17] S.H. Khan and J.K. Kim, Common fixed points of two nonexpansive mappings by a modified faster iteration scheme, Bull. Korean Math. Soc. 47(5) (2010): 973–985.
[18] M.O. Osilike and S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpensive mappings, Math. Comput. Model. 32(10) (2000) 1181–1191.
[19] S.S. Abed and Z.M.M. Hasan, Convergence comparison of two schemes for common fixed points with an application, Ibn AL-Haitham J. Pure Appl. Sci. 32(2) (2019) 81–92.
[20] S.S. Abed and K.E.A. Sada, Common fixed points in modular spaces, Ibn Al-Haitham J. Pure Appl. Sci. (2018) 500–509.
 
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 119-127
  • Receive Date: 10 February 2020
  • Revise Date: 04 October 2020
  • Accept Date: 09 October 2020