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

## DOI:

https://doi.org/10.26713/cma.v14i1.1917## Keywords:

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

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

\begin{align*}

L(x,y,z)

&=\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)\}.

\end{align*}

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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## References

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## How to Cite

*Communications in Mathematics and Applications*,

*14*(1), 21–36. https://doi.org/10.26713/cma.v14i1.1917

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