Author
Yisheng Song
Other affiliations: Henan Normal University, Tianjin Polytechnic University, Hong Kong Polytechnic University
Bio: Yisheng Song is an academic researcher from Chongqing Normal University. The author has contributed to research in topics: Banach space & Tensor. The author has an hindex of 29, co-authored 99 publications receiving 2282 citations. Previous affiliations of Yisheng Song include Henan Normal University & Tianjin Polytechnic University.
Papers published on a yearly basis
Papers
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TL;DR: Fixed point and coincidence results are presented for single-valued hybrid generalized φ-weak contractions T,S defined on complete metric spaces.
162 citations
TL;DR: In this paper, the authors extend some classes of structured matrices to higher-order tensors and discuss their relationships with positive semi-definite tensors, and some other structured tensors.
Abstract: In this paper, we extend some classes of structured matrices to higher-order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. The potential links of such structured tensors with optimization, nonlinear equations, nonlinear complementarity problems, variational inequalities and the non-negative tensor theory are also discussed.
152 citations
TL;DR: In this article, it was shown that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector.
Abstract: In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and that a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.
137 citations
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TL;DR: It is shown that every principal sub-tensor of such a structured Tensor is still a structured tensor in the same class, with a lower dimension, and the potential links of such structured tensors with optimization, nonlinear equations, non linear complementarity problems, variational inequalities and the non-negative tensor theory are discussed.
Abstract: In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. The potential links of such structured tensors with optimization, nonlinear equations, nonlinear complementarity problems, variational inequalities and the nonnegative tensor theory are also discussed.
136 citations
TL;DR: In this article, it was shown that a tensor is an S-tensor if and only if the tensor complementarity problem is feasible, and each Q-Tensor is a S-Tensor.
Abstract: The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonlinear complementarity problem. In this paper, it is proved that a tensor is an S-tensor if and only if the tensor complementarity problem is feasible, and each Q-tensor is an S-tensor. Furthermore, the boundedness of solution set of the tensor complementarity problem is equivalent to the uniqueness of solution for such a problem with zero vector. For the tensor complementarity problem with a strictly semi-positive tensor, we proved the global upper bounds for solution of such a problem. In particular, the upper bounds keep in close contact with the smallest Pareto $H-$($Z-$)eigenvalue.
95 citations
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TL;DR: In this paper, a generalisation of the Banach contraction mapping principle is introduced, and the result extends two existing generalisations of the same principle, and they support their result by an example.
Abstract: Here we introduce a generalisation of the Banach contraction mapping principle. We show that the result extends two existing generalisations of the same principle. We support our result by an example.
373 citations
TL;DR: In this article, the generalized weak contractive condition in partially ordered complete b-metric spaces was shown to hold for four mappings satisfying generalized weak contractsive condition, and the results extended and improved several comparable results in existing literature.
Abstract: We prove some common fixed point results for four mappings satisfying generalized weak contractive condition in partially ordered complete b-metric spaces. Our results extend and improve several comparable results in the existing literature
237 citations
TL;DR: It is shown that self-mappings S, T on a complete partial metric space X have a common fixed point if it is a generalized weak ϕ -contraction.
223 citations
TL;DR: It is established that these mappings necessarily have a unique common fixed point in complete metric spaces and this result generalizes an existing result in metric spaces.
210 citations
Book•
01 Mar 2000
TL;DR: Hadic and Pap as discussed by the authors discussed the convergence of Newton's method under unified conditions and the existence and non-existence of approximate fixed points in Generalized Convex Spaces (GCS).
Abstract: Preface On the Semilocal Convergence of Newton's Method Under Unifying Conditions Inequalities and Fixed Points in Menger Convex Metric Spaces Applications of the Perov's Fixed Point Theorem to Delay Integro-Differential Equations On Vector Equilibrium Problems with Multifunctions Fixed Points in Generalised Metric Spaces and the Stability of a Cubic Functional Equation Continuous Selection and Coincidence Theorems on Product G-Convex Space Sensitivity Analysis of Solution Set for a New Class of Generalised Implicit Quasi-Variational Inclusions Fixed Points in Probabilistic-Quasi-Metric Spaces Common Fixed Point Theorems for Condensed Mappings The Strongly Convergence Theorems of Fixed Points for Local Strictly F-Pseudocontractive On Generalised Non-linear Variational Inequalities A Note on a Paper of Hadic and Pap The Ishiwaka and Mann Iteration Methods On Certain Applications of Leray-Schauder Alternate Remarks on Concepts of Generalised Convex Spaces Generic Existence and Non-Existence of Approximate Fixed Points General System of Relaxed g-?-r-Pseudococoercive Non-linear Variational Inequalities and Projection Methods Three-Step Iteration Methods with Errors for Non-expansive Mappings in Uniformly Convex Banach Spaces On Nonnegative Linear Composite Games of NTU-Game Probabilistic Contractor and Non-linear Operator Equations with Set-Valued Operator in Probabilistic Normed Spaces Index.
192 citations