| Fixed point theory is a vital part of nonlinear functional analysis.And it is one of significant research objects for scholars.In this paper,we mainly explore the common fixed point theorems under the conditions of Banach algebra and weak compatibility.The full text is divided into three chapters:In the first chapter,we introduce the knowledge background,the present research situation and the significance of studying.Then,we describe the work arrangement of this paper.In the second chapter,we mainly study the common fixed point theorem in cone metric spaces with Banach algebras.Under the condition of removing the continuity of mappings and the normality of cones,we not only introduce some new contractive conditions,but also give some new expansive conditions.We also explore the common fixed point which is existed and unique,and verify the correctness of the results by an example.These conclusions generalize a few fixed point theorems in metric spaces.In the third chapter,we explore the common fixed point by using the weakly compatible conditions of mapping pairs in complete S-metric space.First,we construct some new contraction conditions.Then,we prove a few common fixed point theorems which is new by using compressive conditions and get the common fixed point which is unique.Finally,we give an example to verify the effectiveness of the conclusions,which generalize and improve the existing related conclusion. |
