GENERALIZED STUDY OF UNIQUE FIXED POINTS AND COMMUTING SELFMAPS

 Some common fixed point theorems related to complete and compact metric space are proved in the present paper. Which includes the fixed point theorems given by  B. E. Rhoades [31] , G. Jungck [21], G. Das et al. [9], and U. P. Dolhare [ 12, 13, 14, 15 ]. Fixed points for selfmappings, in complete metric spaces, are obtained by using weakly commuting pairs and commuting mappings. We have extended and generalized the results obtained by  K. Goebel and W. A. Kirk and  proved fixed point theorems for selfmaps. Fixed point theorems for selfmappings satisfying weakly contractive conditions, involving altering distance, in complete metric space are also studied.