Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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COMPOSITE IMPLICIT RANDOM ITERATIONS FOR APPROXIMATING COMMON RANDOM FIXED POINT FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE RANDOM OPERATORS

  • Received : 2008.09.12
  • Published : 2011.01.31
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Abstract

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

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Acknowledgement

Supported by : Council of Scientific and Industrial Research(CSIR)

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