A New Method For Solving Split Common Fixed Points

The split equality fixed point problem is an important non-linear problem that is broader than the split feasibility problem,the convex feasible problem,and the split common fixed point problem,the split equality problem is a hot topic in nonlinear functional analysis.The split equality fixed point problem has been widely used in intensity adjustment radiotherapy,domain decomposition of PDE,optimal cybernetics and game theory in medical treatment.At present,the split equality fixed point problem has been widely concerned by scholars in Hilbert space,but most of the results only obtain weak convergence,and some strong convergence can only be obtained under the condition of semi-compact mapping.Therefore,in this paper,strong convergence of the split equality fixed point problem for strict pseudo-compression mapping in the Hilbert space is obtained without semi-compact constraint;In addition,another iterative algorithm is constructed in Hilbert space to study the strong convergence of the split equality fixed point problem for quasi pseudo contractive mapping semigroups:First,the research status and significance of split equality fixed point problem of are briefly described;briefly on the research status of the split equality fixed point problem of operator semigroups.Secondly,a new iterative algorithm is constructed in real Hilbert space to obtain strong convergence for split equality fixed point problems for k-strict pseudo-contractive mappings.Finally,a new iterative algorithm is constructed in real Hilbert space to obtain strong convergence for the split equality fixed point problem for pseudo-contractive semigroups.