We characterise the weak $$^*$$ symmetric strong diameter 2 property in Lipschitz function spaces by a of its predual, Lipschitz-free space. call this new decomposable octahedrality and study duality with general. For Banach space to be decomposably octahedral it is sufficient that dual has property. Whether also necessary condition remains open.

This article provides novel analytical results for the Rice function, the incomplete Toronto function and the incomplete Lipschitz-Hankel Integrals. Firstly, upper and lower bounds are derived for the Rice function, Ie(k, x). Secondly, explicit expressions are derived for the incomplete Toronto function, TB(m,n, r), and the incomplete Lipschitz-Hankel Integrals of the modified Bessel function o...

in this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional brownian motion in a hilbert space. we establish the existence and uniqueness of mild solutions for these equations under non-lipschitz conditions with lipschitz conditions being considered as a special case. an example is provided to illustrate the theory

‎in this work we prove malliavin differentiability for the solution to an sde with locally lipschitz and semi-monotone drift‎. ‎to prove this formula‎, ‎we construct a sequence of sdes with globally lipschitz drifts and show that the $p$-moments of their malliavin derivatives are uniformly bounded‎.

We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in...

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...

We give a very simple proof of the caracterization of Lipschitz regularity of a function by the size of its Haar coefficients. It is well known that given a real function I periodic with period 27r satisfying a Lipschitz 0: condition for 0 < 0: ::::; 1, its kth Fourier coefficient is bounded by Ikl-a . More precisely, the following result holds (see for example Chapter 12 of [9]). (A) Let I be ...

This note presents an implicit function theorem for generalized equations, simultaneously generalizing Robinson’s implicit function theorem for strongly regular generalized equations and Clarke’s implicit function theorem for equations with Lipschitz-continuous mappings.

In computer graphics, the rendering of shading, mist, texture, etc., may require the generation of shading-oo in image luminace or chrominance. This can be mathematically modeled as the construction of a gradual numeric function from a partially deened function. The Lips-chitz condition is an appropriate requirement for gradualness of a function; futhermore it has the advantage of being deened ...

In this paper, global optimization (GO) Lipschitz problems are considered where the multi-dimensional multiextremal objective function is determined over a hyperinterval. An efficient one-dimensional GO method using local tuning on the behavior of the objective function is generalized to the multi-dimensional case by the diagonal approach using two partition strategies. Global convergence condi...