Common Fixed Point Theorems Satisfying Generalized (ψ,ϕ)- Weak Contraction in Metric Spaces
. Preeti
Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana, 124021, India.
Manoj Kumar *
Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana, 124021, India.
. Poonam
Department of Mathematics, Gc, Bissar, Akbarpur, Nuh, India.
*Author to whom correspondence should be addressed.
Abstract
In this manuscript, we shall prove a common fixed point theorem for four weakly compatible self-maps \(\check{Z}\), \(\check{H}\), \(\check{Ω}\) and \(\check{K}\) on a metric space (M, \(d^{\circ}\)) satisfying the following generalized (\(\psi\), \(\phi\)- weak contraction:
Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.
Keywords: Fixed point, weakly compatible maps, E.A. property, (CLR) property, generalized (ψ,ϕ)- weak contraction