Almost $\psi$-contractions under binary relations with applications to nonlinear elastic beam equations

In this paper, we establish a fixed point theorem for strict almost -contractions under binary relations in Kaleva-Seikkala's type fuzzy b-metric spaces.By introducing two novel lemmas, we provide new proofs that differ from the original ones in metric spaces.The results obtained herein not only strengthen but also extend the scope of pre-existing fixed point theorems in the relevant literature.Additionally, As a practical application, the existence and uniqueness of solutions to nonlinear elastic beam equations are effectively demonstrated thereby bridging the theoretical and applied aspects of this study.