Best proximity points and fixed points for p-summing maps

Abstract

We have found a new type of a contractive condition that ensures the existence and uniqueness of fixed points and best proximity points in uniformly convex Banach spaces. We provide some examples to validate our results. These results generalize some known results from fixed point theory.

Best proximity points of p-cyclic orbital Meir–Keeler contraction maps

“…The distances between the consecutive sets appear to be equal. It is in contrast to the conditions investigated in [21] and [24], where the conditions, which ensure existence and uniqueness of the best proximity points, hold true for sets with different distances between them.…”

EXISTENCE OF FIXED POINT AND BEST PROXIMITY POINT OF $p$-CYCLIC ORBITAL CONTRACTION OF BOYD-WONG TYPE

“…Now for each k, dist(A i , A i+1 ) + ǫ 0 ≤ T (8).By letting k −→ ∞ and by Proposition 12, b), we have…”

On Ω Class of Mappings in a p-Cyclic Complete Metric Space

“…This statement is plain but significant when we compare with the results of Bryant. Attendantly, the concept of the cyclic contractions has been investigated densely by a considerable number of authors who bring several variants of the notion and derive a number of interesting results (see, e.g., [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein).…”