In this note we introduce strongly Lipschitz p-integral operators, strongly Lipschitz p-nuclear operators and Lipschitz p-nuclear operators. It is shown that for a linear operator, the Lipschitz p-nuclear norm is the same as its usual p-nuclear norm under certain conditions. We also prove that the Lipschitz 2-dominated operators and the strongly Lipschitz 2-integral operators are the same with ...

We consider the classical inverse mapping theorem of Nash and Moser from angle some recent development by Ekeland authors. Geometrisation tame estimates coupled with certain ideas coming variational analysis when applied to a directionally differentiable produces very general surjectivity result and, if injectivity can be ensured, expected Lipschitz-like continuity inverse. also present brief a...

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved an estimate of constant computed. The main contribution work establishment equivalence relationship between graph convergence sequence strongly their mappings, respectively, to given by using no...

In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without prior knowledge constant mapping. Finally, some numerical examples provided to illustrate efficiency advantag...

Let M and N be doubly connected Riemann surfaces with $${\mathscr {C}}^{1,\alpha }$$ boundaries nonvanishing conformal metrics $$\sigma $$ $$\wp respectively, assume that is a smooth metric bounded Gauss curvature $${\mathcal {K}}$$ finite area. Assume {H}}^\wp (M, N)$$ the class of all {W}}^{1,2}$$ homeomorphisms between {E}}^\wp : {\mathcal N)\rightarrow {\mathbf {R}}$$ Dirichlet-energy funct...

‎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.

and Applied Analysis 3 the uniform r-prox-regularity C is equivalent to the convexity of C. Moreover, it is clear that the class of uniformly prox-regular sets is sufficiently large to include the class p-convex sets, C1,1 submanifolds possibly with boundary of H, the images under a C1,1 diffeomorphism of convex sets, and many other nonconvex sets; see 6, 8 . Now, let us state the following fac...

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 first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...