We prove some coupled fixed point theorems for mappings satisfying different contractive conditions on complete cone metric spaces.

Matthews [12] introduced a new distance P on a nonempty set X, which he called a partial metric. The purpose of this paper is to present some fixed point results for weakly contractive type mappings in ordered partial metric space. An application to nonlinear fractional boundary value problem is also presented.

We study some common results in C*-algebra-valued $S_b$-metric spaces. We also present an interesting application of an existing and unique result for one type of integral equation.

The aim of the present paper is to state and prove some convergence theorems for the Mann and Ishikawa iteration schemes involving $C^{*}$ -algebra-multi-valued contractive mappings in the setting of convex $C^{*}$ -algebra-valued metric spaces. The convergence theorems of the proposed iterations to a common fixed point of finite and infinite family of such mappings are also established.