Common fixed point theorems for four self maps satisfying generalized (, )-weak contraction in metric space

In this manuscript, we shall prove a common fixed point theorem for four weakly compatible self-maps P,Q,R and Son a metric space (M,d & lowast;) satisfying the following generalized (psi,phi)-weak contraction: psi(d & lowast;(Ru,Sv))<=psi(triangle(u,v))-phi(triangle(u,v)) where triangle(u,v) = max{d(& lowast;)(Ru,Sv),d(& lowast;)(Ru,Pu),d(& lowast;)(Sv,Qv),1/2[d(& lowast;)(Pu,Sv) +d(& lowast;)(Qv,Ru)], d(& lowast;)(Pu,Ru)d(& lowast;)(Qv,Sv)/1 +d(& lowast;)(Ru,Sv), d(& lowast;)(Pu,Sv)d(& lowast;)(Qv,Ru)/1 +d(& lowast;)(Ru,Sv), d(& lowast;)(Ru,Pu)[1 +d & lowast;(Ru,Qv) +d & lowast;(Sv,Pu)1 +d & lowast;(Ru,Pu) +d & lowast;(Sv,Qv)]}. Also, we have proved common fixed point theorems for the above mentioned contraction using weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.