Common Fixed Point Results for Four Self - Maps Satisfying Contractive Inequality of Integral Type in Metric Spaces

This manuscript consists a common fixed point result for four weakly compatible self-maps ˆ P, ˆ Q, ˆ S, ˆ T on a metric space (M, d∗) satisfying the following contractive inequality of integral type: Z d∗( ˆ Tμ, ˆ Sν) 0 ξ(t)dt ≤ β(d∗(μ, ν)) Z Δ1(μ,ν) 0 ξ(t)dt, where (ξ, β) ∈ ξ1 × ξ3 and for all μ, ν in M. Δ1(μ, ν) = max{d∗( ˆ Tμ, ˆ Sν), d∗( ˆ Tμ, ˆ Pμ), d∗( ˆ Sν, ˆ Qν), 1 2 [d∗( ˆ Pμ, ˆ Sν) + d∗( ˆ Qν, ˆ Tμ)], d∗( ˆ Pμ, ˆ Tμ).d∗( ˆ Qν, ˆ Sν) 1 + d∗( ˆ Tμ, ˆ Sν) , d∗( ˆ Pμ, ˆ Sν).d∗( ˆ Qν, ˆ Tμ) 1 + d∗( ˆ Tμ, ˆ Sν) , d∗( ˆ Tμ, ˆ Pμ)[ 1 + d∗( ˆ Tμ, ˆ Qν) + d∗( ˆ Sν, ˆ Pμ) 1 + d∗( ˆ Tμ, ˆ Pμ) + d∗( ˆ Sν, ˆ Qν) ]}. 150 South East Asian J. of Mathematics and Mathematical Sciences Also, some common fixed point results for the above mentioned weakly compatible self - maps along with E.A. property and (CLR) property are proved. A suitable illustrative example is also provided to support our result