New fixed point results for asymptotic contractions and its application to cantilever beam problems

S. Karmakar, H. Garai, A. Chanda, L. K. Dey

In this article, we deal with some interesting variants of asymptotic contractions, namely Reich type and Chatterjea type weak asymptotic contractions defined on the usual metric spaces. We derive a couple of fixed point results concerning such contractions. Moreover, we look over the existence of solutions to a fourth-order two-point boundary value problem which is a particular type of cantilever beam problems. Furthermore, we construct numerical examples to justify our obtained results.