Let S : A→ B and T : A→ B be given non-self mappings, where A and B are non-empty subsets of a metric space. As S and T are non-self mappings, the equations Sx = x and T x = x do not necessarily have a common solution, called a common fixed point of the mappings S and T . Therefore, in such cases of nonexistence of a common solution, it is attempted to find an element x that is closest to both ...

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Theta$- contraction mappings andto prove some best proximity point results for t...

The aim of this paper is to prove the existence and convergence theorems for cyclic contractions. We introduce a notion called proximally complete pair (A,B) on a metric space, which unify the earlier notions that are used to prove the existence of a best proximity point for a cyclic contraction. By observing geometrical properties on a Hilbert space, we introduce Pythagorean property and use t...

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...

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,...

In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and nonexpansive mappings Banach show the existence best proximity points for both classes. Further, mappings, prove point theorem on starshape sets. As consequence, also obtain some fixed theorems. Finally, give examples to illustrate our main results.