In this article, we first introduce the concept of T-mapping of a finite family of strictly pseudononspreading mapping, and we show that the fixed point set of the T-mapping is the set of common fixed points ofand T is a quasi-nonexpansive mapping. Based on the concept of a T-mapping, we propose a simultaneous iterative algorithm to solve the split equality problem with a way of selecting the stepsizes which does not need any prior information about the operator norms. The sequences generated by the algorithm weakly converge to a solution of the split equality problem of two finite families of strictly pseudononspreading mappings. Furthermore, we apply our iterative algorithms to some convex and nonlinear problems. MSC: 47H09; 47H05; 47H06; 47J25
In this article, the M-eigenvalue of fourth-order partially symmetric tensors is estimated by choosing different components of M-eigenvector. As an application, some upper bounds for the M-spectral radius of nonnegative fourth-order partially symmetric tensors are discussed, which are sharper than existing upper bounds. Finally, numerical examples are reported to verify the obtained results.
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