Results on Hardy–Rogers Contraction

With a proper metrizability approach that preserves completeness of a metric space, Hardy–Rogers contraction may be observed as a Banach contraction. Consequently, the same conclusion holds for Kannan, Reich and Chatterjea contractions along with several their modifications. Theoretical results are substantiated with several examples which additionally validate the independence between some contractive conditions. Rate and factor of convergence of iterative process in a newly defined metric space is studied along with a numerical example claiming a slight advantage of the proposed approach.