In this article, we first introduce the concept of T-mapping of a finitefamily of strictly pseudononspreading mapping "Equation missing"<!-- image only, no MathML or LaTex -->, and we show that the fixed point set of theT-mapping is the set of common fixed points of"Equation missing"<!-- image only, no MathML or LaTex --> and T is a quasi-nonexpansive mapping.Based on the concept of a T-mapping, we propose a simultaneousiterative algorithm to solve the split equality problem with a way of selectingthe stepsizes which does not need any prior information about the operatornorms. The sequences generated by the algorithm weakly converge to a solution ofthe split equality problem of two finite families of strictly pseudononspreadingmappings. Furthermore, we apply our iterative algorithms to some convex andnonlinear problems.MSC: 47H09, 47H05, 47H06, 47J25.

A linear‐implicit finite difference scheme is given for the initial‐boundary problem of GBBM‐Burgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second‐order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is efficient and accurate.

Inspired by symmetric Cauchy tensors, we define fourth-order partially symmetric Cauchy tensors with their generating vectors. In this article, we focus on the necessary and sufficient conditions for the M-positive semi-definiteness and M-positive definiteness of fourth-order Cauchy tensors. Moreover, the necessary and sufficient conditions of the strong ellipticity conditions for fourth-order Cauchy tensors are obtained. Furthermore, fourth-order Cauchy tensors are M-positive semi-definite if and only if the homogeneous polynomial for fourth-order Cauchy tensors is monotonically increasing. Several M-eigenvalue inclusion theorems and spectral properties of fourth-order Cauchy tensors are discussed. A power method is proposed to compute the smallest and the largest M-eigenvalues of fourth-order Cauchy tensors. The given numerical experiments show the effectiveness of the proposed method.