by generalizing the well known guiding function method. Such an approach can be found in several works, however, under some heavier assumptions. For example, in [M] f is assumed to be locally lipschitzian and the guiding function to be C. In [GP] f needs to be of the Caratheodory type only, while the corresponding guiding function must be still C. In fact, in [GP] the more general, multivalued ...

We prove the existence of a continuous selection of the multivalued map ) η , ξ ( → AF ) η , ξ ( , where AF ) η , ξ ( is the set of all mild solutions of the Cauchy problem x” ∈ Ax + F(t, x) , x (0) = ξ , x (0) = η assuming that F is Lipschitzian with respect to x and A is the infinitesimal generator of a strongly cosine family of linear operators on a Banach space E. AMS 2000 Subject Classific...

Abstract In this article, we obtain some fixed-point results involving α -admissibility for multivalued F -contractions in the framework of partial $\mathfrak{b}$ b -metric spaces. Appropriate illustrations are provided to support main results. Finally, an application is developed by demonstrating existence a...

In the present paper, we establish first relation between perturbation of upper Fredholm and strictly singular, then lower semi-Fredholm cosingular linear relations. Most importantly in Theorem 3.4, show that P(F?(X,Y)) coincides with SC(X,Y).We bring to light, relationship essential spectra a multivalued operator its selection

Each lower semi-continuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E* called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone" relations on Ex E*, and that each of these is also a maximal monotone relation. Furthermore, it is proved that of de...

A Lefschetz-type coincidence theorem for two maps f, g : X → Y from an arbitrary topological space to a manifold is given: Ifg = λfg , that is, the coincidence index is equal to the Lefschetz number. It follows that if λfg 6= 0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y...

We define the multivalued Reich (G, ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f : [0, 1] → Lρ and then give the modular analogue to Kelisky-Rivlin theorem. c ©2016 All rights reserved.

We establish a fixed point theorem for a continuous function f : X → E, where E is a Banach space and X ⊆ E. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.