On Fixed Points of Asymptotically Regular Mappings

Abstract

Some results on fixed points of asymptotically regular mappings are obtained in complete metric spaces and normed linear spaces.The structure of the set of common fixed points is also discussed in Banach spaces. Our work generalizes essentially known results of Das and Naik, Fisher, Jaggi, Jungck, Rhoades, Singh and Tiwari and several others.

Coincidence and common fixed points of hybrid contractions

“…Some fixed point theorems for commuting and weakly commuting mappings may be found in [3][4][5] and [14][15][16][17][18]20]. If fz ^ gz, then we obtain the contradiction d(fz, gz) < d(fz, gz).…”

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

“…On the other hand, in [20], Rhoades et al introduced the concept of asymptotically regular sequences in metric spaces and proved a fixed point theorem using this concept.…”

Fixed points of asymptotically regular multivalued mappings

“…A sequence {x n } in X is said to be asymptotically T-regular if d(x n , Tx n ) -> 0. The presence of a sequence {x n } for which d{x n , Tx n ) -> 0 is related to some property of T (see [3], [7], [8], [24], [25], and [27]) and hence is exploited to obtain fixed points of T. The aim of the present paper is to bring out the thrust of a similar assumption for multivalued mappings. The weakly dissipative multivalued mappings recently introduced by Aubin and Siegel in [3] satisfy such an assumption.…”