Ulam-Hyers stability and well-posedness of fixed point problems for \(\alpha\)-\(\lambda\)-contraction mapping in metric spaces. (English) Zbl 1429.54054

Kutbi, Marwan Amin; Sintunavarat, Wutiphol

Abstr. Appl. Anal. 2014, Article ID 268230, 6 p. (2014).

Summary: 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.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54E40	Special maps on metric spaces

Keywords:

Ulam-Hyers stability; fixed point; generalized contraction; \(\alpha\)-\(\lambda\)-contraction mapping

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