... Rus introduced the concept of theory of a metric fixed ¸ point theorem and used this theory for the case of multivalued contraction see For the singlevalued case, see The purpose of this paper ... Proceedings of the 9th International Conference on Fixed Point Theory and Its Applications, Yokohama Publishing, to appear Fixed Point Theory and Applications I A Rus, The theory of a metrical fixed point ... —Programul IDEI1239” for the provided financial support The authors are grateful for the reviewer s for the careful reading of the paper and for the suggestions which improved the quality of this work...