Fixed point, its geometry, and application via ω‐interpolative contraction of Suzuki type mapping

Abstract

In fixed point theory, interpolation is acknowledged in numerous areas of research, for instance, earth sciences, metallurgy, surface physics, and so on because of its prospective applications in the estimation of signal sensation analysis. As a result, it is interesting to investigate the fixed point and fixed circle (disc) utilizing interpolative techniques via partial b‐metric spaces in which non‐trivial as well as real generalizations are feasible. We define some improved interpolative contractions to create an environment for the existence of a fixed point and fixed circle and solve a two‐point boundary value problem related to a differential equation of second order. The obtained conclusions are validated by providing illustrative examples. Determining the fixed point of a non‐self mapping, the uniqueness of the fixed point and fixed circle, and the study of fractal interpolants would also be a fascinating investigation in the time to come.

Editorial of the special issue on modelling, analysis, and applications

“…Another paper proposes a $$$ {b}_g $$$‐multiplicative metric space, inspired by the concept of nonlinear elastic matching, generalized metrics, and multiplicative triangle inequality, to generalize the distance between 2 points and $$$ G $$$‐metric between 3 points [36]. Additionally, a study applies interpolation techniques to create an environment for the existence of fixed point and circle and to solve a two‐point boundary value problem, associated to a differential equation of second order [37].…”