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In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X×X×X → X and g : X → X satisfying a nonlinear contraction based on φ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results.

The notion of partial metric space [1], represented by the abbreviation PMS, departs from the usual metric spaces due to removing the assumption of self-distance. In other words, in PMS self-distance needs not to be zero. This interesting distance function is defined by Matthews [1], as a generalization metric to study in computer science, in particular, to get a more efficient programs in comp...

– For the system of d-dim stochastic differential equations, dXε(t)= b(X(t))dt + εσ(X(t))dW(t), t ∈ [0,1], Xε(0)= x0 ∈Rd, where b(x) and σ(x) are smooth except possibly along the hyperplane {(x1, . . . , xd);x1 = 0}, we shall demonstrate that the natural setup of its large deviation principle is to consider the probability ε2 logP(‖Xε − φ‖< δ, ‖uε − ψ‖ < δ, ‖ ε − η‖< δ)∼−I (φ,ψ,η) of the triple...

We consider the nonlinear degenerate elliptic-parabolic-hyperbolic equation ∂tg(u)−∆b(u)− div Φ(u) = f(g(u)) in (0, T )× Ω, where g and b are nondecreasing continuous functions, Φ is vectorial and continuous, and f is Lipschitz continuous. We prove the existence, comparison and uniqueness of entropy solutions for the associated initial-boundary-value problem where Ω is a bounded domain in RN . ...

Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework for contracting edges of a graph (merging vertices into super-vertices) with the goal of preserving pairwise distances as accurately as possible. Formally, given an edge-weighted graph, the contraction s...

So far, we have considered only a single real field φ with a φ 4-interaction. The theory can, however, easily be extended to a set of N identical real fields φ α with α = 1,. .. , N. This extension does not produce any new Feynman diagrams. Additional work arises from the fact that the coupling constant g becomes now a tensor g αβγδ , and each momentum integral in a Feynman diagram is accompani...

Let ψ : X → Y be a proper morphism with connected fibers from a smooth projective variety X onto a normal variety Y , i.e. a contraction. If −KX is ψ-ample, then ψ is said to be an extremal contraction and if moreover Pic(X)/ψ(Pic(Y )) ≃ Z then ψ is said to be an elementary extremal contraction or a Fano-Mori contraction. Usually contractions are divided into two types: birational and of fiber ...

If the contraction T is a Toeplitz operator on H2 or A2 induced by an analytic function φ, we then denote the resulting space by H(φ). Similarly, if T is the Toeplitz operator on H2 or A2 induced by a conjugate analytic symbol φ, then we denote the resulting space by H(φ). In the context of Hardy spaces, H(φ) and H(φ) are called sub-Hardy Hilbert spaces by Sarason in [6]. We thus arrive at the ...

We show how the nearly bi-maximal mixing scenario comes out naturally from gauged SO(3) F flavor symmetry via spontaneous symmetry breaking. An interesting relation between the neutrino mass-squared differences and the mixing angle, i.e., ∆m 2 µe /∆m 2 τ µ ≃ 2|U e3 | 2 is obtained. The smallness of the ratio (or |U e3 |) can also naturally be understood from an approximate permutation symmetry....