Common Fixed Point Theorems for Weakly Compatible Maps Satisfying Integral Type Contraction in G-Metric Spaces - Kumar, Narinder; Kumar, Manoj; Ashish, (Communications in Mathematics and Applications, 2023)
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.