In this paper, we obtain an existence result for the integral boundary value problems of nonlinear fractional q-difference equations on half-line using Schauder?s fixed point theorem.

In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli’s theorem. Three examples are also provided to illustrate our main results.

A generalization of the classical Leray-Schauder fixed point theorem, based on the infinitedimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. MIRAMARE – TRIESTE May 2007 [email protected]; [email protected]

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

In this article, a generalization of a Kakutani-Fan fixed point theorem for multi-valued mappings in Banach spaces is proved under weaker upper semi-continuity condition and it is further applied to derive a generalized version of Krasnoselskii’s fixed point theorem and some nonlinear alternatives of Leray-Schauder type for multi-valued closed mappings in Banach spaces. RESUMEN En este artículo...

The main object of this paper is to investigate the existence solutions for a self-adjoint coupled system nonlinear second-order ordinary differential equations equipped with nonlocal multi-point boundary conditions on an arbitrary domain. We apply Leray–Schauder alternative, Schauder fixed point theorem and Banach contraction mapping principle in order derive results, which are then well-illus...

In this paper, by using the Schauder fixed point theorem and the Banach contraction principle, we investigate existence and uniqueness of solutions for a class of multi-point boundary value problems of nonlinear fractional q-difference equations. As applications, two examples are presented to show the effectiveness of the obtained results.

*Correspondence: [email protected] 1Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain Full list of author information is available at the end of the article Abstract We prove a new fixed point theorem of Schauder type, which applies to discontinuous operators in noncompact domains. In order to do so, we...