We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu-B...

In this paper, we study the existence and uniqueness solution and investigate the conditions that make it almost-periodic solution for BAM neural networks with retarded delays. The existence of solution established by using Schauder fixed point theorem. The uniqueness established by using Banach fixed point theorem. Moreover we study the parametric stability of such a solution. Also we illustra...

Abstract. In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green’s function, a nonlinear alternative of Leray–Schauder-type, Guo–Krasnoselskii’s fixed point theorem in a cone and the Banach...

Nonexpansive mappings have been studied extensively in recent years by many authors.The first fixed point theorem of a general nature for nonlinear nonexpansive mappings in noncompact setting were proved independently by Browder [8] and Gohde [12]. Later on, Kirk [17] proved the same results under slightly weaker assumptions. A fundamental problem in fixed point theory of nonexpansive mappings ...

Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

In this paper, we establish a sufficient condition for the controlla-bility of impulsive quasi-linear fractional mixed Volterra-Fredholm-type inte-grodifferential equations in Banach spaces. The results are obtained by using Banach contraction fixed point theorem combined with the fractional calculus theory.

*Correspondence: [email protected] Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Avenida Reina Mercedes, Seville, 41012, Spain Abstract We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator ...