We study connectivity preserving multivalued functions [10] between digital images. This notion generalizes that of continuous multivalued functions [6, 7] studied mostly in the setting of the digital plane Z. We show that connectivity preserving multivalued functions, like continuous multivalued functions, are appropriate models for digital morpholological operations. Connectivity preservation...

An important aspect of data modeling is the identification of entities or objects and their associated attributes. An attribute may be single-valued or multivalued. During database design, the designer usually has to represent all attributes in relational tables that only allow single-valued cells. A number of authors (1, 3, 5, 6) advocate the notion that multivalued attributes are essentially ...

In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f -MK -pair mappings and f -CJM-pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfie...

A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results ext...

Here A : D(A) ⊆H →H is a maximal monotone operator (possibly multivalued) in a real Hilbert space H , D(A) is its domain, a,b ∈ D(A), f ∈ L2(0,T ;H), and p, r are two continuous functions from [0,T] to R. In [10, 11], Barbu proved the existence of the solution in the case p ≡ 1, r ≡ 0. The author considered the boundary value problems u′′(t) ∈Au(t) + f (t), a.e. t ∈ (0,T), u(0) = a, u(T) = b, (...

The quasilinear degenerate evolution equation of parabolic type d(Mv) dt + L(Mv)v = F (Mv), 0 < t ≤ T considered in a Banach space X is written, putting Mv = u, in the form du dt + A(u)u 3 F (u), 0 < t ≤ T , where A(u) = L(u)M−1 are multivalued linear operators in X for u ∈ K, K being a bounded ball ‖u‖Z < R in another Banach space Z continuously embedded in X. Existence and uniqueness of the l...

We present coincidence points results for multivalued f nonexpansive mappings in the setting of nonstarshaped domain of q-normed space which is not necessarily a locally convex space. As application, an invariant approximation result is also obtained. Our results improve and extend the results of Bano, Khan and Latif [1], Hussain [4], Latif and Tweddle [7], Rhoades [11], Sahab, Khan and Sessa [...

We present an elementary proof that, for a multivalued map φ : R R with nonempty connected values and monotone margins, the existence of a periodic orbit of any order k > 1 implies the existence of periodic orbits of all orders. This generalizes a very recent result of this type in terms of scalar ordinary differential equations without uniqueness, due to F. Obersnel and P. Omari, obtained by m...