Abstract

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.

Keywords: Asymptotic contractions; orbital continuity; cantilever beam problems; boundary value problems.

MSC: 47H10, 54H25

DOI: 10.57016/MV-anbl7148

Pages:  260$-$271     

Volume  74 ,  Issue  4 ,  2022