We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic, including applications to coincidence points. An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a diffe...

This paper extends Krein-Rutman's theorem on linear operators leaving an invariant cone in infinite-dimensional Banach spaces to multivalued convex functions. The result is applied to obtain necessary and sufficient conditions for global controllability and reachability of nonlinear discrete-time systems described by convex processes.

The main purpose of this article is to give a relationship between Fredholm multivalued linear operators and the demicompact relation; we provide some sufficient conditions on inputs closable block operator matrix ensure generalized demicompactness its closure. Our results generalize many known ones in literature.

In this paper we will present an abstract point of view on iterative approximation schemes of fixed points for multivalued operators. More precisely, we suppose that the algorithms are convergent and we will study the impact of this hypothesis in the theory of operatorial inclusiosns: data dependence, stability and Gronwall type lemmas. Some open problems are also presented.

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.

*Correspondence: [email protected] 2National School of Applied Sciences, Cadi Ayyad University, Marrakesh, Morocco Full list of author information is available at the end of the article Abstract This paper provides new common fixed point theorems for pairs of multivalued and single-valued mappings operating between ordered Banach spaces. Our results lead to new existence theorems for a system of ...

In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.