In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresp...

and Applied Analysis 3 which is called the general variational inequality, introduced and studied by Noor 19 . It has been shown that the minimum of a class of differentiable functions can be characterized by the general variational inequality of type 2.3 . B If g ≡ I, the identity operator, then 2.1 reduces to find u ∈ C and w ∈ A u such that 〈F u w,v − u〉 ≥ 0, ∀v ∈ C, 2.4 which is known as th...

Let K be a multivalued map from the interval [0, 1] to R. On its graph, denoted by Gr(K), another multivalued map F is defined. Its values are closed subsets of R. The map F , called an orientor field, gives rise to a differential inclusion ẋ(t) ∈ F (t, x(t)). The inclusion is called viable, if for every (t0, x0) ∈ Gr(K) there is a global absolutely continuous forward trajectory x : [t0, 1] → R...

In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with domF = X, is finite only if F is single-valued. This implies in particular that for a sublinear multivalued mapping the inner and the outer norms cannot be finite simultaneously. AMS 2000 Subject Classification: 49J53, 47H04, 54C60.