Let K be a closed convex subset of a Hilbert space H and T : K ⊸ K a nonexpansive multivalued map with a unique fixed point z such that {z} = T (z). It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to z.

Gangbo and McCann showed that optimal transportation between hypersurfaces generally leads to multivalued optimal maps – bivalent when the target surface is strictly convex. In this paper we quantify Hölder continuity of the bivalent map optimizing average distance squared between arbitrary measures supported on Euclidean spheres.

Assume that X is a metrizable separable space, and each clopen-valued lower semicontinuous multivalued map Φ : X ⇒ Q has a continuous selection φ : X → Q. Our main result is that in this case, X is a σ-space. We also derive a partial converse implication, and present a reformulation of the Scheepers Conjecture in the language of continuous selections.

In the present paper‎, ‎we introduce the concept of generalized multivalued $F$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including Nadler's‎.

Article history: Received 19 February 2009 Received in revised form 28 October 2011 Accepted 21 December 2011 Available online 23 December 2011

The authors show that there is a generalization of Rodrigues’ formula for computing the exponential map exp: so(n)→SO(n) from skewsymmetric matrices to orthogonal matrices when n ≥ 4, and give a method for computing some determination of the (multivalued) function log: SO(n) → so(n). The key idea is the decomposition of a skew-symmetric n×n matrix B in terms of (unique) skew-symmetric matrices ...

Abstract In this paper, we consider fractional neutral differential equations with multipoint boundary value conditions involving Hadamard derivatives and integrals. We obtain the existence uniqueness of solution equation by using several fixed point theorems, also Ulam–Hyers stability solution. addition, study inclusion problem prove when multivalued map has convex values. give examples to ill...

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...