Fixed Point Theorem in Banach Space

Abstract

The purpose of this paper is to obtain a common fixed theorem in Banach space using a contractive type condition Work on common fixed point have done by many authors  such as  Iseki K., Kannan R. , Rus I.A., Sehgal S.L , Yen C.L , Singh S.L , Fisher B. , Rhoades B.E. and Sessa S., Ray, B.K. and Chatterjee H. ,Sharma P.L. and Rajput ,S.S, Sharma P.L. and Bajaj N.;, etc. have also established interesting results on common fixed point. We prove let(X,d) be a Banach space. Let   P , S and  T  are three self mapping  as P,  S and   T  :   X   →  X  satisfy  in   the conditions

         || SPx -TPy||  ≤ α       + β 

                             +γ                                         

for all x,y in X and  α , β , γ are reals and  α+β+γ  < 1. Futher assume that either SP=PS or TP =  PT.Then S,T and P have a common unique fixed point in X.