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 http://dx.doi.org/10.22436/jnsa.012.10.03

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.

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Keywords

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

MSC

•  47H09
•  47H10

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