ABSTRACT

A new inclusion problem is introduced using generalized Cayley operator and we call it Cayley inclusion problem. We also study its corresponding resolvent equation problem. By using a generalized resolvent operator and generalized Yosida approximation operator, first we establish a fixed point formulation for Cayley inclusion problem. An algorithm is defined to find the solution of Cayley inclusion problem. An existence and convergence result is proved. Secondly, we have shown the equivalence of Cayley inclusion problem with a resolvent equation. We define an iterative algorithm with some of its equivalent forms for solving resolvent equation problem. A numerical example is constructed and a convergence graph is shown by using MATLAB program.

摘要

使用广义凯莱算子引入了一个新的包含问题，我们称之为凯莱包含问题。我们还研究了它对应的求解方程问题。通过使用广义分解算子和广义Yosida近似算子，我们首先建立了凯莱包含问题的不动点公式。定义了一种算法来找到凯莱包含问题的解决方案。证明了存在性和收敛性结果。其次，我们证明了凯莱包含问题与求解方程的等价性。我们定义了一个迭代算法及其一些等效形式来解决求解方程问题。用MATLAB程序构造了一个数值例子并给出了收敛图。