We construct two counter-examples related to Fréchet differentiability in infinite dimensions. The first one gives a convex Lipschitzian function on a Banach space such that its convolution with a given measure is Fréchet differentiable only on a measure zero set. The second one gives a Borel function on a space with a Gaussian measure such that it is Lipschitzian along the Cameron–Martin subsp...

We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the sta...

Fixed point theorems for generalized Lipschitzian semigroups are proved in puniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp , and in Sobolev spaces Hk,p , for 1<p <∞ and k≥ 0.

Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. An application of this result to prove the validity of the Euler Lagrange equation for w is presented.

We study the convergence of Ishikawa iteration process for the class of asymptotically κ-strict pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Weak convergence theorem is established. We also obtain a strong convergence theorem by using hybrid projection for this iteration process. Our results improve and extend the corresponding results announced by...

An identity for the Chebychev functional is presented in which a Riemann-Stieltjes integral is involved. This allows bounds for the functional to be obtained for functions that are of bounded variation, Lipschitzian and monotone. Some applications are presented to produce bounds for moments of functions about a general point γ and for moment generating functions.

In this paper, we present the convergence of Krasnoselskii Mann iterative process for common fixed points pointwise Lipschitzian evolution family bounded nonlinear operators on a Banach space ℜ .

This article gives a really vital and curiously inequality on Jain-Saraswat’s functional discrimination in terms of the Hellinger Bhattacharya by taking into thoughtL-Lipschitzian functions. Encourage, we outlined few results utilizing inferred with numerical confirmation.