Approximation of Fixed Points of Contactive Operators by a Stochastic Iterative Algorithm
Onwukwe Ijioma, B.C.Ugoala , V.N.Madukpe
Abstract
We prove a strong convergence result using stochastic iterative scheme with contractive operators associated with error terms. The iterative process is faster, simpler which improves other algorithms, and for the class of mapping in a more global sense.
Keywords
Contractive operator
stochastic algorithm
fixed point
strong
convergence.
References
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Lipschitzian strictly Pseudo contractive mappings. Proc. Am. Math.
Soc., 99: 283-288.
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Applied To A WalrasianEquilibrium Model” IJAM vol. 5,No. 1, pp
35-44, 2012.
[10] O. Ijioma“ A Stochastic Iteration Method for A Class of Monotone
Variational Inequalities In Hilbert Space” International Journal of
Scientific and Statistical Computing (IJSSC), vol.(8), Issue(1): 2020
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Optimization of Random Systems”
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Fixed
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(http://dx.doi.org/10.4236/am.212.312A293 )
4, 5 06-510 (1953)
[2] Reich, S: Weak Convergence Theorem for non expansive mappings
in Banach spaces. J. Math. Anal. Appl. 67, 274-276 (1979)
[3] Shahazad, N. Zegeye, H : Approximating of common point of fixed
points of a pseudo-contractive mapping and zero of sum of monotone
mappings.Fixed point Theory Appl.,85.(2014)
[4] Zamfirescu, T.: Fixed point Theorems in metric spaces, Arch.Math
(Basel, 23(1972), 292-298
[5] Khan, Safeer. H. Fixed Points of Contractive-Like Operators by a
Faster
Iterative Process, Int. Journal of Math. Compl, Nat.
and Phy Eng. Vol 7, No.: 12, 2013
[6] C.O. Imoru, M.O.Olatinwo, On the stability of Picard and Mann
Iteration
processes, Carpathian Journal of Mathematics ,
19,155-160, 2003
[7] Browder, F.E., Non linear mapping of nonexpansive and accretive
type in Banach spaces. Bull. Am. Math. Soc. 73,875-882 (1967).
[8] Chidume, C.E. 1987. Iterative approximation of fixed point of
Lipschitzian strictly Pseudo contractive mappings. Proc. Am. Math.
Soc., 99: 283-288.
[9] O. Ijioma and A.C. Okoroafor “A Stochastic Approximation Method
Applied To A WalrasianEquilibrium Model” IJAM vol. 5,No. 1, pp
35-44, 2012.
[10] O. Ijioma“ A Stochastic Iteration Method for A Class of Monotone
Variational Inequalities In Hilbert Space” International Journal of
Scientific and Statistical Computing (IJSSC), vol.(8), Issue(1): 2020
[11] L. Ljung, G. Pfugand H. Walk. “ Stochastic Approximation and
Optimization of Random Systems”
[12] Ya.I.Alber, C.E. Chidume, Jinlu Li. “Stochastic Approximation
Method for
Fixed
Point
Problems” Applied
Mathematics,
2012,3,2123-2132
(http://dx.doi.org/10.4236/am.212.312A293 )
