Existence and Convergence Theorems of Fixed Points of a Lipschitz Pseudo-contraction by an Iterative Shrinking Projection Technique in Hilbert Spaces

The aim of this paper is to provide some existence theorems of a Lipschitz pseudo-contraction by the way of a hybrid shrinking projection method involving some necessary and sufficient conditions. The method allows us to obtain a strong convergence iteration for finding some fixed points of a Lipschitz pseudocontraction in the framework of real Hilbert spaces. In addition, we also provide certain applications of the main theorems to confirm the existence of the zeros of a Lipschitz monotone operator along with its convergent results.