We will prove existence and uniqueness theorems for solution of the boundary value problem x∆∆(t) = f(t, xσ(t)), x(a) = A, x(σ2(b)) = B for t in a measure chain T. In one of our results we use upper and lower solutions to prove the existence of a solution to this boundary value problem (BVP). We then use this result to show that if for each fixed t, f(t, x) is strictly increasing in x, then thi...

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

We consider the follow-the-leader particle approximation scheme for a [Formula: see text] scalar conservation law with non-negative compactly supported initial datum and concave flux, which is known to provide convergence towards entropy solution corresponding Cauchy problem. two novel contributions this theory. First, we prove that one-sided Lipschitz condition satisfied by approximate density...

our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...

Let f be a Lipschitz mapping of a separable Banach space X to a Banach space Y. We observe that the set of points at which f is diierentiable in a spanning set of directions but not G^ ateaux diierentiable is-directionally porous. Since Borel-directionally porous sets, in addition to being rst category sets, are null in Aronszajn's (or, equivalently, in Gaussian) sense, we obtain an alternative...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

This paper focuses on a class of stochastic functional differential equations with infinite delay and non-Lipschitz coefficients. Under one-sided super-linear growth conditions, this establishes the existence uniqueness strong solutions Markov properties segment processes. additional assumption non-degeneracy diffusion coefficient, exponential ergodicity for process is derived by using asymptot...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.