We generalize the result of Pre？i？ in metric-like spaces by proving some common fixed point theorems for Pre？i？ type mappings in metric-like spaces. An example is given which shows that the generalization is proper. 1. Introduction and Preliminaries Let be any metric space, and let be any mapping; then is said to be a contraction on if there exists such that A point is called a fixed point of if . Banach [1] proved that every contraction on a complete metric space has a unique fixed point and this result is known as the Banach contraction principle. There are several generalizations of this famous principle. One such generalization is given by Pre？i？ [2, 3]. When studying the convergence of some particular sequences, Pre？i？ [2, 3] proved the following theorem. Theorem 1. Let be a complete metric space, a positive integer, and a mapping satisfying the following contractive type condition: for every , where are nonnegative constants such that . Then there exists a unique point such that . Moreover, if are arbitrary points in and for , then the sequence is convergent and . Note that the -step iterative sequence given by (3) represents a nonlinear difference equation. In view of Pre？i？ theorem, it is obvious that if this sequence is convergent (which is ensured by the Pre？i？ theorem) then the limit of the sequence is a fixed point of . The result of Pre？i？ is generalized by several authors, and some generalizations and applications of Pre？i？ theorem can be seen in [4–15]. On the other hand, Matthews [16] introduced the notion of a partial metric space as a part of the study of denotational semantics of a dataflow network. In this space, the usual metric is replaced by a partial metric with an interesting property that the self-distance of any point of space may not be zero. Further, Matthews showed that the Banach contraction principle is valid in a partial metric space and can be applied in program verifications. O'Neill [17] generalized the concept of a partial metric space a bit further by admitting negative distances. The partial metric defined by O'Neill is called the dualistic partial metric. Heckmann [18] generalized it by omitting the small self-distance axiom. The partial metric defined by Heckmann is called a weak partial metric. Recently, Amini-Harandi [19] generalized the partial metric spaces by introducing the metric-like spaces. Amini-Harandi introduced the notion of a -Cauchy sequence and completeness of metric-like spaces and proved some fixed point theorems in such spaces. In this paper, we prove some common fixed point theorems for Pre？i？
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