In a recent paper by H.X. Cao, J.H. Zhang and Z.B. Xu a α-Lipschitz operator from a compact metric space into a Banach space A is defined and characterized in a natural way in the sence that F : K → A is a α-Lipschitz operator if and only if for each σ ∈ X∗ the mapping σoF is a α-Lipschitz function. The Lipschitz operators algebras L(K,A) and l(K,A) are developed here further, and we study thei...

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuit...

We establish the existence and uniqueness of strong solutions to stochastic porous media equations driven by Lévy noise on a $$\sigma $$ -finite measure space $$(E,{\mathcal {B}}(E),\mu )$$ , with Laplacian replaced negative definite self-adjoint operator. The coefficient $$\Psi is only assumed satisfy increasing Lipschitz nonlinearity assumption, without restriction $$r\Psi (r)\rightarrow \inf...

in this paper‎, ‎we consider a general integral operator $g_n(z).$ the main object of the present paper is to study some properties of this integral operator on the classes $mathcal{s}^{*}(alpha),$ $mathcal{k}(alpha),$ $mathcal{m}(beta),$ $mathcal{n}(beta)$ and $mathcal{kd}(mu,beta).$‎

We discuss 1-Lipschitz aggregation operators with a given affine section. The greatest 1-Lipschitz aggregation operator as well as the greatest quasicopula with a given affine section are explicitly given. In the case of a horizontal section it is shown to be a singular copula. A similar result for the smallest (quasi-)copula with a given horizontal section is also included.

This paper is concerned with the study of a penalization-gradient algorithm for solving variational inequalities, namely, find x ∈ C such that 〈Ax, y − x〉 ≥ 0 for all y ∈ C, where A : H → H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ : H → ∪ { ∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalization parameter ...

In this paper we obtained tensor product sum of Toeplitz and multiplication operator induced dynamical system on analytic Lipschitz spaces.