In this paper, we introduce a new concept of $\alpha$-$\psi$-contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
Samet, B., Vetro, C., Vetro, P. (2012). Fixed point theorems for $\alpha$-$\psi$-contractive type mappings. NONLINEAR ANALYSIS, 75(4), 2154-2165 [10.1016/j.na.2011.10.014].
Fixed point theorems for $\alpha$-$\psi$-contractive type mappings
VETRO, Calogero;VETRO, Pasquale
2012-01-01
Abstract
In this paper, we introduce a new concept of $\alpha$-$\psi$-contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
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