NONLINEAR ERGODIC THEOREMS FOR WIDELY MORE GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES

Authors

  • MAYUMI HOJO Shibaura Institute of Technology, Tokyo 1358548, Japan
  • WATARU TAKAHASHI Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan

Keywords:

Banach limit, generalized hybrid mapping, Hilbert space, nonexpansive mapping, nonspreading mapping, strongly asymptotically invariant net

Abstract

In this paper, using strongly asymptotically invariant nets, we first obtain some properties of widely more generalized hybrid mappings ina Hilbert space. Then, using the idea of mean convergence by Shimizu and Takahashi [24, 25], we prove a nonlinear ergodic theorem for widely more generalized hybrid mappings in a Hilbert space. This generalizes the Kawasaki and Takahashi nonlinear ergodic theorem.

Additional Files

Published

03/25/2014

Issue

Vol. 5 No. 1 (2014): JNAO

Section

Research Articles

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Copyright (c) 2010 Journal of Nonlinear Analysis and Optimization: Theory & Applications

Creative Commons License

This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.