Subgradient mappings have many roles in variational analysis, such as the formulation of optimality conditions and, in the special case of normal cone mappings, the statement and analysis of variational inequalities and related expressions. Central to the study of perturbations of solutions to systems of conditions in which subgradient mappings appear are concepts of generalized differentiation...

This paper is motivated by an astonishing result of H. Alzer and S. Ruscheweyh published in 2001, which states that the intersection classes two-variable Gini means Stolarsky equal to class power means. The form two-parameter expressed terms functions. They can naturally be generalized so-called Bajraktarević Cauchy Our aim show these two functional means, under high-order differentiability ass...

In this paper, we obtain a version of Ekeland's variational principle for interval-valued functions by means the Dancs-Hegedüs-Medvegyev theorem (Dancs et al. (1983) [14]). We also derive two versions involving generalized Hukuhara Gâteaux differentiability as well bifunctions. Finally, apply these new to fixed point theorems, optimization problems, Mountain Pass Theorem, noncooperative games, ...

S. M. Robinson published in 1980 a powerful theorem about solutions to certain “generalized equations” corresponding to parameterized variational inequalities which could represent the first-order optimality conditions in nonlinear programming, in particular. In fact, his result covered much of the classical implicit function theorem, if not quite all, but went far beyond that in ideas and form...

In a standard free end nonsmooth control problem in finite dimensional state space, a nonsmooth maximum principle is proved, in which the adjoint inclusion is sharper than the usual one. For end constrained problems, the same result holds, provided conditions ensuring local controllability are satisfied. The adjoint inclusion is expressed by means of a type of generalized gradient of the pseudo...

Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0, T ] (T > 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existe...

Here we consider the ordinary and fractional approximation of functions by sublinear positive operators with applications to generalized convolution type expressed integrals such as Choquet Shilkret ones. The is under differentiability Caputo, Canavati Iterated-Caputo types. We produce Jackson inequalities basic initial conditions. So our way quantitative producing their right hand sides involv...

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.