Fixed point results of weakly contraction mappings in partially ordered b-metric spaces

Abstract

Abstract Objectives We explored the results of fixed point, coincidence point and coupled coincidence point for the mappings in an ordered metric spaces. Our results generalized and extended the well-known results in the literature. Some numerical examples are provided for justifying the results obtained. Result Some fixed point results are found for a self mapping in a partially ordered b-metric space which satisfies a generalized week contraction condition. Furthermore, these results are extended for two self mappings for obtaining coincidence point, coupled coincidence point and coupled common fixed point in the same context. A few examples are presented to support the findings.

Keywords

• $$({\hat{\phi }}, {\hat{\psi }})$$ ( ϕ ^ , ψ ^ ) -Weak contractions
• Fixed point
• Coincidence point
• Compatible mappings
• Coupled coincidence point
• Coupled common fixed points