Common Fixed Point Theorems for Weakly Compatible Maps Satisfying Integral Type Contraction in G-Metric Spaces




Fixed point, G-metric space, Coincidence point, Weakly compatible maps, E.A property, (CLRg) property


The main purpose of this manuscript is to prove a common fixed point theorem for two weakly compatible maps satisfying the following integral type contraction in \(G\)-metric space:
\int^{G(\mathcal{F}x,\mathcal{F}y,\mathcal{F}z)}_0\varphi (t)dt\le \alpha \int^{L(x,y,z)}_0\varphi (t)dt,
for all \(x,y, z\in X\), where
&=\max\{G(gx, gy, gz), G(gx, \mathcal{F}x, \mathcal{F}x), G(gx, \mathcal{F}y, \mathcal{F}y),\\
&\qquad\quad \ \ G(gy, \mathcal{F}y, \mathcal{F}y),  G(gy, \mathcal{F}x, \mathcal{F}x), G(gz, \mathcal{F}z, \mathcal{F}z),\\
&\qquad\quad \ \ G(gz, \mathcal{F}x, \mathcal{F}x), G(gz, \mathcal{F}y, \mathcal{F}y)\}.
Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-mappings along with E.A property and (\(\mathit{CLR}_g\)) property.


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How to Cite

Kumar, N., Kumar, M., & Ashish. (2023). Common Fixed Point Theorems for Weakly Compatible Maps Satisfying Integral Type Contraction in G-Metric Spaces. Communications in Mathematics and Applications, 14(1), 21–36.



Research Article