# Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces

Volume 12, Issue 10, pp 644--655
Publication Date: June 03, 2019 Submission Date: February 04, 2019 Revision Date: April 03, 2019 Accteptance Date: April 07, 2019
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### Authors

Sahar Mohamed Ali Abou Bakr - Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt.

### Abstract

This paper proves the existence of a unique common fixed point of two self mappings defined on complete cone quasi metric space $\mathfrak{C}$ with respect to Banach algebra, consequently in particular, it proves the existence of only one fixed point of a generalized cyclic Banach algebra contraction and a cyclic Banach algebra Kannan type mappings with respect to a couple of non empty subsets $(A, B)$ of a complete cone quasi metric space $\mathfrak{C}$. These existences extend the fixed point results of the attached references and then generalized the corresponding classical results in usual Banach spaces as well.

### Share and Cite

##### ISRP Style

Sahar Mohamed Ali Abou Bakr, Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 10, 644--655

##### AMA Style

Abou Bakr Sahar Mohamed Ali, Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces. J. Nonlinear Sci. Appl. (2019); 12(10):644--655

##### Chicago/Turabian Style

Abou Bakr, Sahar Mohamed Ali. "Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces." Journal of Nonlinear Sciences and Applications, 12, no. 10 (2019): 644--655

### Keywords

• Quasi metric spaces
• fixed point theorems
• $\{a,b,c\}$ generalized contractions
• generalized $\phi$ weak contractions
• cyclic contraction mappings

•  47H09
•  47H10

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