Common Fixed Point Theorem for (\(\phi\),\(\mathfrak{F}\))–Multi-Valued Mappings in Cone b-Metric Spaces over Banach Algebra
R. Jahir Hussain
Jamal Mohamed College (Autonomous) - Affiliated to Bharathidasan University, Tiruchirapplli-620020, Tamil Nadu, India.
K. Maheshwaran *
Jamal Mohamed College (Autonomous) - Affiliated to Bharathidasan University, Tiruchirapplli-620020, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
In the present paper, we introduced the concept of generalized multi-valued contraction mappings, via the class functions \(\Phi\) and \(\Psi\) Also we proved some fixed point results for (\(\phi\),\(\mathfrak{F}\))- multi-valued mappings on cone b-metric spaces over Banach algebra \(\mathfrak{V}\). The conditions for existence and uniqueness of the fixed point are investigated. We give an example to support our main result.
Keywords: Cone b-Metric space, multi-valued mappings, Banach algebra