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: \[ ^G(Fx,Fy,Fz)_0φ (t)dtα ^L(x,y,z)_0φ (t)dt, \] for all \(x,y, zX\), where align* L(x,y,z) &={G(gx, gy, gz), G(gx, Fx, Fx), G(gx, Fy, Fy), & G(gy, Fy, Fy), G(gy, Fx, Fx), G(gz, Fz, Fz), & G(gz, Fx, Fx), G(gz, Fy, Fy)}. align* Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-mappings along with E.A property and (\(CLR_g\)) property.