The xed point result in Mustafa-Sims metrical structures obtained by Karapinar and Agarwal[Fixed Point Th. Appl., 2013, 2013:154] is deductible from a corresponding one stated in terms ofanticipative contractions over the associated (standard) metric space.

The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.

Machine-learning solutions to classification, clustering and matching problems critically depend on the adopted metric, which in the past was selected heuristically. In the last decade, it has been demonstrated that an appropriate metric can be learnt from data, resulting in superior performance as compared with traditional metrics. This has recently stimulated a considerable interest in the to...

the purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fi xed point on geraghty-contraction. in this paper,de nitions of approximate -pair fi xed point for two maps tα , sα and theirdiameters are given in a metric space.