On common fixed points of compatible mappings in metric and Banach spaces

Abstract

ABSTRACT. We prove a number of results concerning the existence of common fixed points of a family of maps satisfying certain contractive conditions in metric and Banach spaces. Results dealing with the stucture of the set of common fixed points of such maps are also given. Our work is an improvement upon the previously known results.

Discontinuity and R-weak commutativity in fixed point consideration on non complete fuzzy metric spaces

“…all [4] was extended by Sharma and Deshande [39]. Cho [3] also extended, generalized and fuzzified some known results in fuzzy metric spaces metric spaces probabilistic metric spaces and uniform spaces ( [10], [17], [20], [25], [28], [32]). He proved a common fixed point theorem for mappings under the condition of continuity and compatibility of type (α) on complete fuzzy metric spaces.…”

Common fixed point theorems for compatible self-maps of Hausdorff topological spaces

“…Compatible maps, in turn, proved productive in producing common fixed points and further generalizations of Banach's theorem: [2,6,8,9,10,11,12,14,15,16,18,19,20]. On the other hand, the concept of proper orbits now provides new results, and a means of extending a bevy of known results.…”

Fixed Point Theorems on Product of Compact Metric Spaces

“…[15]), if and only if they are coordinatewise weak commutating at every point of X. Notice that Definitions 1-3 with n = 1 are the standard ones of commuting, weakly commuting (see [13]) and asymptotically commuting [17] (also called compatible [6]) maps.…”