This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Hölder type, respectively, hold. Furthermore, we apply the ...

A mapping $f\colon X\to Y$ between metric spaces is termed little Lipschitz if the function ${\rm lip}\, f\colon [0,\infty ]$, $${\rm f(x)=\liminf_{r\to 0}\frac{{\rm diam}\,f(B(x,r))}{r},$$ finite at every point. We prove that for

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...

The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others special cases. This paper presents picture for relationship between points Moreau proximal mapping solutions that satisfies some kinds monotonicity Lipschitz-type condition.

Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for t...

It is known that there are several approaches to define a Sobolev class for Banach valued functions. We compare the usual definition via weak derivatives with Reshetnyak–Sobolev space and Newtonian space; in particular, we provide sufficient conditions when all three agree. Also, revise difference quotient criterion property of Lipschitz mapping preserve it acting as superposition operator.

Motivated by problems arising in decentralized control problems and non-cooperative Nash games, we consider a class of strongly monotone Cartesian variational inequality (VI) problems, where the mappings either contain expectations or their evaluations are corrupted by error. Such complications are captured under the umbrella of Cartesian stochastic variational inequality problems and we consid...

Abstract In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak spaces. The primary aim study is to a necessary sufficient condition operator induced by diffeomorphism particular, detailed information derived from boundedness, i.e., bi-Lipschitz continuity mapping that induces follows mapping. idea proof determine norm characteristic functions, e...

We investigate typical properties of nonexpansive mappings on unbounded complete hyperbolic metric spaces. For two families metrics uniform convergence bounded sets, we show that the mapping is a Rakotch contraction every subset and there set which mapped into itself by this mapping. In particular, obtain in setting has unique fixed point can be reached iterating Nevertheless, it turns out not ...