In this note, we establish and improve some results on fixed point theory in topological vector spaces. As a generalization of contraction maps, the concept of quasi contraction multivalued maps on a topological vector space will be defined. Further, it is shown that a quasi contraction and closed multivalued map on a topological vector space has a unique fixed point if it is bounded value.

The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of D − orić and Lazović 2011 for a multivalued map on a metric space satisfying Ćirić-Suzuki-type-generalized contraction. Further, as a special case, we obtain a generalization of an important common fixed point theorem of Ćirić 1974 . Existence of a common soluti...

This paper is concerned with a class of Wλ0 pseudomonotone maps given by Kasyanov et al. (2010, 2006) [2,15]. We indicate that its main character of passing to a subsequence in classical definition is meaningless. Then, we show that Wλ0 pseudomonotone map is the same as a class of known pseudomonotone maps (Theorem 2) rather than its generalization (cf. Kasyanov et al. (2010) [2] lines 2–3, p. ...

The paper addresses the problem of recovering a pseudoconvex function from the normal cones to its level sets that we call the convex level sets integration problem. An important application is the revealed preference problem. Our main result can be described as integrating a maximally cyclically pseudoconvex multivalued map that sends vectors or “bundles” of a Euclidean space to convex sets in...

In this work, we examine the problem of constructing and maintaining a map of an autonomous vehicle’s environment for the purpose of navigation, using evidential reasoning. The inherent uncertainty in the origin of measurements of sensors demands a probabilistic approach to processing, or fusing, the new sensory information to build an accurate map. In this paper, the map is based on a two-dime...

The deenitions of isolating block, index pair, and the Conley index, together with the proof of homotopy and additivity properties of the index are generalized for discrete multivalued dynamical systems. That generalization provides a theoretical background of numerical computation used by Mischaikow and Mrozek in their computer assisted proof of chaos in the Lorenz equations, where nitely repr...

Zilber's Exponential Algebraic Closedness conjecture (also known as Nullstellensatz) gives conditions under which a complex algebraic variety should intersect the graph of exponential map semiabelian variety. We prove special case where has dominant projection to domain map, for abelian varieties and tori. Furthermore, in situation intersection is 0-dimensional, we exhibit structure by parametr...

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...

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps. Keywords—Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.