### Coincidence and Fixed Points for Multivalued Mappings in Incomplete Metric Spaces with Applications

#### Abstract

In the present paper, firstly, we review the notion of

$\mathrm{R}$-complete metric spaces, where $\mathrm{R}$ is a binary

relation (not necessarily a partial order). This notion lets us to

consider some fixed point theorems for multivalued mappings in

incomplete metric spaces. Secondly, as motivated by the recent work

of Wei-Shih Du (On coincidence point and fixed point theorems for

nonlinear multivalued maps, {\it Topology and its Applications} 159

(2012) 49--56), we prove existence of coincidence points and fixed

points of a general class of multivalued mappings satisfying a new

generalized contractive condition in $\mathrm{R}$-complete metric

spaces which extends some well-known results in the literature. In

addition, this article consists of several non-trivial examples

which signify the motivation of such investigations. Finally, we

give an application to the nonlinear fractional boundary value

equations.

#### Full Text:

PDF### Refbacks

- There are currently no refbacks.