Generalized Study of Commuting Self-Maps and Fixed Points

In this paper, some common fixed point theorems are proved related to complete & compact metric space, in which the fixed point theorems in G. Jungck [17], B. E. Rhoades [5], G. Das & J. P. Dabata [16] and U. P. Dolhare. [ 9, 10, 11, 34] as a special case. By using weakly commuting pairs, commuting maps & find out fixed point for self-maps in complete metric space. We proved some fixed point results for self-mappings satisfying weakly contractive conditions with fixed point results involving altering distance in complete metric space. . In this paper we extend and generalize the results obtained by K. Goebel and W. A. Kirk and prove fixed point theorem for self maps.