in this paper, we unify, extend and generalize some results on coupled fixed point theorems of generalized φ- mappings with some applications to fixed points of integral type mappings in cone metric spaces.

In this paper, we unify, extend and generalize some results on coupled fixed point theorems of generalized φ- mappings with some applications to fixed points of integral type mappings in cone metric spaces.  

In this paper, new concepts of monotonicity, namely (Φ, ρ)-monotonicity, (Φ, ρ)-pseudo-monotonicity and (Φ, ρ)-quasi-monotonicityare introduced for functions defined in Banach spaces. Series of necessary conditions are also given that relate (Φ, ρ)-invexity and generalized (Φ, ρ)-invexity of the function with (Φ, ρ)monotonicity and generalized (Φ, ρ)-monotonicity of its gradient.

Generation of a quasi-contractive semigroup by generalized Ornstein-Uhlenbeck operators ℒ = −∆ + ∇Φ · ∇ − G V c|x|−2 in the weighted space L2(RN, e−Φ(x)dx) is proven, where Φ ∈ C2(RN, R), C1(RN, RN), 0 ≤ C1(RN) and c > 0. The proofs are carried out an application L2-weighted Hardy inequality bilinear form techniques.

where capG(S, S̄) is the total weight of the edges crossing from S to S̄ = V − S. We show that the minimum generalized eigenvalue λ(LG, LH) of the pair of Laplacians LG and LH satisfies λ(LG, LH) ≥ φ(G,H)φ(G)/8, where φ(G) is the usual conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to λ(LG, LH). The inequality complements a...