Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation

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• 作者：Dhananjay GOPAL ; ^{dg@ashd.svnit.ac.in" class="auth_mail" title="E-mail the corresponding author} ; ^{gopaldhananjay@yahoo.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：fixed points ; nonlinear fractional differential equations ; periodic points
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：36
• 期：3
• 页码：957-970
• 全文大小：353 K

文摘

In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from α-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.