A concept of g-monotone mapping is introduced, and some fixed and common fixed point theorems for g-non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to Agarwal et al. 2008 .

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In this paper some existence results of positive solutions for the following singular nonlinear third order two-point boundary value problem: ((a, b), [0, +∞)), f ∈ C([a, b] × (0, +∞), [0, +∞)), α(t) may be singular at t = a, b and f (t, x) may be singular at x = 0.

This paper discusses the existence of at least one or two nondecreasing positive solutions for the following singular nonlinear third-order differential equationmay be singular at t = a, b and f (t, s) may be singular at s = 0. Green's function and the fixed-point theorem of cone expansion and compression type are utilized. To illustrate the results, four nontrivial examples are included.