Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.

关于带有附加条件的Chatterjea类型非扩张映射的一些结果

比较Reich型非扩张映射、Chatterjea型非扩张映射和(c)映射,得到一些结论。在0<c≤b这个假设的前提下,证明了C hatterjea型非扩张映射是渐近正则的,并且在UCED Banach空间中,Chatterjea型非扩张映射具有一个不动点。最后,证明了Chatterjea型非扩张映射在轨道上是连续的也是k-连续的。

度量空间和锥度量空间中的若干不动点定理

给出了度量空间和锥度量空间中的若干不动点定理.利用这些不动点定理,统一并推广了度量空间和锥度量空间中的若干经典的不动点定理.

模度量空间下的不动点定理

推广了模度量空间,针对一类被称之为Chatterjea映射,在适当的条件下,建立了映射T具有不动点的存在性和唯一性结果.