Two systems of fractional order functional and neutral functional differential equations with infinite delay are studied in this article, and some sufficient conditions for existence of unique solutions for these two systems are established by Banach fixed point theorem.

A fixed point theorem is proved for non-self multi-valued mappings in a metrically convex complete metric space satisfying a slightly stronger contraction condition than in Rhoades [3] and under a weaker boundary condition than in Itoh [2] and Rhoades [3].

In this paper we investigate the existence and uniqueness of solutions of a class of partial impulsive hyperbolic differential equations with fixed time impulses involving the Caputo fractional derivative. Our main tool is a fixed point theorem.

*Correspondence: [email protected] 4Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, 46022, Spain Full list of author information is available at the end of the article Abstract The aim of this paper is to show that a soft metric induces a compatible metric on the collection of all soft points of the absolute soft set, when the set of param...

But which fixed point of Γ do we want? We would like to take the “least” fixed point, in the sense that we want C[[while b do c]] to give a non-⊥ result only when required by the intended semantics. (For example, we want C[[while true do skip]]σ =⊥ for all σ.) The rest of this lecture will expand on this notion of least fixed point, with a look at the underlying theory of partial orders. Iterat...

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not involving any metrics. We demonstrate its applications to the metric, ultrametric and topological cases, and to ordered abelian groups and fields.

A continuum is an arboroid if it is hereditarily unicoherent and arcwise connected. A metric arboroid is a dendroid. A generalized dendrite is a locally connected arboroid. Among other things, we shall prove that a locally connected continuum X is a generalized dendrite if and only if X has the fixed point property for continuous, closed set-valued mappings.

*Correspondence: [email protected]; [email protected] Department of Mathematics, Dong Thap University, Dong Thap, Dong Thap, Vietnam Abstract In this paper, we prove a fixed point theorem on a 2-metric space and show that the main results in Lahiri et al. (Taiwan. J. Math. 15:337-352, 2011) and Singh et al. (J. Adv. Math. Stud. 5:71-76, 2012) may be obtained easily from the axioms...

By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

In this paper, by using Schauder fixed point theorem, we study the existence of at least one positive solution to a coupled system of fractional boundary value problems given by { −D1 0+ y1(t) = λ1a1(t)f(t, y1(t), y2(t)) + e1(t), −D2 0+ y2(t) = λ2a2(t)g(t, y1(t), y2(t)) + e2(t), where ν1, ν2 ∈ (n− 1, n] for n > 3 and n ∈ N , subject to the boundary conditions y 1 (0) = 0 = y (i) 2 (0), for 0 ≤ ...