Using viscosity approximation method, we study strong convergence to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued mappings satisfying the condition ($E$) in the setting of Hilbert space. Our results improve and extend some recent results in the literature.

We will apply the fixed point method for proving the generalized Hyers-Ulam stability of the integral equation $\left(1/2c\right){\int }_{x-ct}^{x+ct}u\left(\tau ,t_0\right)d\tau =u\left(x,t\right)$ which is strongly related to the wave equation.

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we introduced and study the concept of one-local retract in modular metric space. In particular, we investigate the existence of common fixed points of modular nonexpansive mappings defined on nonempty $\omega$-closed $\omega$-bounded subset of modular metric space.