In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive ...In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.展开更多
A new model in nonholonomic mechanics, the Rosen-Edelstein model, has been studied. We prove that the new model is a Lagrange problem in which the action integral ∫t0^t1 Ldt can be made stationary. The theoretical ba...A new model in nonholonomic mechanics, the Rosen-Edelstein model, has been studied. We prove that the new model is a Lagrange problem in which the action integral ∫t0^t1 Ldt can be made stationary. The theoretical basis of nonholonomic mechanics is investigated and discussed. Finally, we give the range of practical applications of the Rosen-Edelstein model.展开更多
We show that an （eventually） strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert＇s projective metric. By applying t...We show that an （eventually） strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert＇s projective metric. By applying the Edelstein contraction theorem, a nonlinear version of the famous Krein- Rutman theorem is presented, and a simple iteration process {T^kx/｜｜T^kx｜｜} （ x ∈ P^＋） is given for finding a positive eigenvector with positive eigenvalue of T. In particular, the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein contraction with respect to Hilbert＇s projective metric. As a result, the nonlinear Perron-Frobenius property of a nonnegative tensor A is reached easily.展开更多
基金supported by Università degli Studi di Palermo (Local University Project ex 60%)
文摘In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10272021 and 10572021） and the Doctoral Programme Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘A new model in nonholonomic mechanics, the Rosen-Edelstein model, has been studied. We prove that the new model is a Lagrange problem in which the action integral ∫t0^t1 Ldt can be made stationary. The theoretical basis of nonholonomic mechanics is investigated and discussed. Finally, we give the range of practical applications of the Rosen-Edelstein model.
基金Acknowledgements The authors would like to thank the anonymous referees for their useful comments and valuable suggestions. This work was supported by the Hong Kong Research Grant Council （Grant Nos. PolyU 501808, 501909, 502510, 502111） and the first author was supported partly by the National Natural Science Foundation of China （Grant Nos. 11071279, 11171094, 11271112）.
文摘We show that an （eventually） strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert＇s projective metric. By applying the Edelstein contraction theorem, a nonlinear version of the famous Krein- Rutman theorem is presented, and a simple iteration process {T^kx/｜｜T^kx｜｜} （ x ∈ P^＋） is given for finding a positive eigenvector with positive eigenvalue of T. In particular, the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein contraction with respect to Hilbert＇s projective metric. As a result, the nonlinear Perron-Frobenius property of a nonnegative tensor A is reached easily.
