New hybrid algorithms for global minimization of common best proximity points of some generalized nonexpansive mappings

Common best proximity points for $(psi-phi)$-generalized weak proximal contraction type mappings

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.

Common best proximity points: global minimization of multi-objective functions

Assume that A and B are non-void subsets of a metric space, and that S : A −→ B and T : A −→ B are given non-self mappings. In light of the fact that S and T are non-self mappings, it may happen that the equations Sx = x and Tx = x have no common solution, named a common fixed point of the mappings S and T . Subsequently, in the event that there is no common solution of the preceding equations,...

Approximating fixed points of generalized nonexpansive mappings

Existence of common best proximity points of generalized $S$-proximal contractions

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

On best proximity points for multivalued cyclic $F$-contraction mappings

In this paper, we establish and prove the existence of best proximity points for multivalued cyclic $F$- contraction mappings in complete metric spaces. Our results improve and extend various results in literature.