Fixed points of \(\omega \)-interpolative Hardy–Rogers contraction and its application in b-metric spaces

Experimental signals, besides numerous real-world problems, need a sensation of smoothness in their traces. So, non-differentiable interpolates in a dense set of points are required to model these signals. Also, fractal interpolation, based on the technique of the iterated function system, is utilized to find solutions to such problems. Motivated by the fact that numerous real-world problems may be restated via fixed point theory, the objective of this work is to bring in and utilize \(\omega \)-interpolative Hardy–Rogers contraction in metric as well as b-metric spaces to establish the non-unique fixed points. We furnish illustrative examples to validate our conclusions and demonstrate the significant fact that the notion of \(\omega \)-admissibility refines the notion of continuity and an \(\omega \)-admissible mapping is \(\omega \)-regular. We conclude the work by solving the system of linear equations.