We will investigate some existence, uniqueness, and Ulam-Hyers stability results for fixed point problems via --contractive mapping of type-() in the framework of -metric spaces. The presented theorems extend, generalize, and unify several results in the literature, involving the results of Samet et al. (2012).

In this paper, we establish some new existence, uniqueness and Ulam-Hyers stability theorems for coincidence problems for two single-valued mappings. The main results of this paper extend the results presented in O. Mleşniţe: Existence and Ulam-Hyers stability results for coincidence problems, J. Nonlinear Sci. Appl., 6 (2013), 108-116. In the last section two examples of application of these results are also given.

Let X, Y be two nonempty sets and s, t : X → Y be two single-valued operators.By definition, a solution of the coincidence problem for s and t is a pair (x * , y * ) ∈ X × Y such thatIt is well-known that a coincidence problem is, under appropriate conditions, equivalent to a fixed point problem for a single-valued operator generated by s and t. Using this approach, we will present some existence, uniqueness and Ulam -Hyers stability theorems for the coincidence problem mentioned above. Some examples illustrating the main results of the paper are also given.

In this paper, we will present some existence and Ulam-Hyers stability results for fixed point and coincidence point problems with multivalued operators using the weakly Picard operator technique in spaces endowed with vector metrics.

The purpose of the work is to present some Ulam-Hyers stability results for the coincidence point problem associated to single-valued and multivalued operators. As an application, an Ulam-Hyers stability theorem for a differential inclusion.