Fixed point theory for contractive mappings satisfying \(\Phi \)-maps in G-metric spaces
The \(\varphi\)-contraction principle in a complete metric space is well known (see [\textit{J. Matkowski}, ''Integrable Solutions of Functional Equations,'' Dissertationes Math., Warszawa 127, 63 p. (1975; Zbl 0318.39005)]; \textit{I. A. Rus}, [Math., Rev. Anal. Numér. Théor. Approximation, Math. 24(47), 175--178 (1982; Zbl 0525.54029) and Generalized Contractions and Applications. Cluj-Napoca: Cluj University Press. (2001; Zbl 0968.54029)]; \textit{J. Jachymski} and \textit{M. Styborski}, Fixed point theory and its applications. Proceedings of the international conference, Bȩddlewo, Poland, August 1--5, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 77, 123-146 (2007; Zbl 1149.47044)]). In this paper a fixed point principle for \(\varphi\)-contractions in a complete G-metric space (see \textit{Z. Mustafa} and \textit{B. Sims}, [J. Nonlinear Convex Anal. 7, No. 2, 286--297 (2006; Zbl 1111.54025)]) is presented. Then a theory [\textit{I. A. Rus}, Fixed Point Theory 9, No. 2, 541--559 (2008; Zbl 1172.54030)] of this metrical fixed point theorem is discussed.
scientific article; zbMATH DE number 5792435