The Fixed Point Property Of Mean Nonexpansive Mapping

For all the time,the fixed point theory has played an important role in the modern mathematics research.It is the basis of modern mathematics,and it has been widely used in applied mathematics and other fields.It is worth mentioning that the study of the fixed point problems plays a decisive role in many fields,such as in the fields of differential equations,quantum mechanics,cybernetics,abstract harmonic analysis and optimization.Since the fixed point theory has a wide range of applications in many fields,the research of the fixed point theory has become the research direction of choice of many mathematicians.In this paper,the existence of the fixed point of the mean nonexpansive mapping is mainly studied by using the geometric properties of Banach spaces,and the theorem of iterative convergence is given.Therefore,it is also profound.The fixed point properties of the mean nonexpansive mappings are discussed in this paper,which are divided into three parts.The main contents are as follows:In the first chapter,we briefly reviews the fixed point theory and the development of the mean nonexpansive mapping,and the fixed point theory in domestic and foreign research present situation has carried on the brief narration.In the second chapter,we discuss the fixed point property of the mean nonexpansive mapping,and verify the existence of fixed points under the mean nonexpansive mapping in a Banach space of a certain geometry.Finally,we study the relationship between the Garcia-Falset constant R(1,X)and the mean nonexpansive mapping T have the fixed point property.In the third chapter,we give three newly defined iterations,and verify the existence of fixed points of the mean nonexpansive mapping T under these three different iterations.We also obtain a sufficient condition that the newly defined iteration converges to the fixed point of T.