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 ...

We introduce the concepts of ∗-diminishing orbital diameters and diminishing orbital diameters for a pair (f ,g) of self mappings in metric spaces and prove common fixed point theorems for these mappings. The results obtained in this paper extend properly the result of Fisher (1978). 2000 Mathematics Subject Classification. 54H25.

Given non-empty subsets A and B of a metric space, let S : A → B and T : A → B be non-self mappings. Taking into account the fact that, given any element x in A, the distance between x and Sx, and the distance between x and Tx are at least d(A,B), a common best proximity point theorem affirms global minimum of both functions x → d(x, Sx) and x → d(x, Tx) by imposing a common approximate solutio...

We show how a d-stress on a piecewise-linear realization of an oriented (non-simplicial, in general) d-manifold in Rd naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of self-stresses in spatial frameworks. The mappings we construct are not linear, but polynomial. In the 1860–70s J. C. Maxwell described an interesting...

We present Kakutani type fixed point theorems for certain semigroups of self maps by relaxing conditions on the underlying set, family of self maps, and the mappings themselves in a locally convex space setting.

We obtain a generalization of the Burns-Krantz rigidity theorem for holomorphic self-mappings of the unit disk in the spirit of the classical Schwarz-Pick Lemma and its continuous version due to L.Harris via the generation theory for one-parameter semigroups. In particular, we establish geometric and analytic criteria for a holomorphic function on the disk with a boundary null point to be a gen...