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We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces. We have applied certain results due to Sahu (2005) to obtain conditions for existence—and to introduce an asymptotic iterative process for construction—of fixed points of these hemicontractions with respect to a new auxiliary operator.

Nearly Contraction Mapping Principle for Fixed Points of Hemicontinuous Mappings