Ulam-Hyers Stability and Well-Posedness of Fixed Point Problems for α-λ-Contraction Mapping in Metric Spaces

Abstract

We study Ulam-Hyers stability and the well-posedness of the fixed point problem for new type of generalized contraction mapping, so called $\alpha$-$\lambda$-contraction mapping. The results in this paper generalize and unify several results in the literature such as the Banach contraction principle.