A fixed point theorem for orbitally continuous functions.

A New Common Fixed Point Theorem for Suzuki Type Contractions via Generalized $Psi$-simulation Functions

In this paper, a new stratification of mappings, which is  called $Psi$-simulation functions, is introduced  to enhance the study of the Suzuki type weak-contractions. Some well-known results in weak-contractions fixed point theory are generalized by our researches. The methods have been appeared in proving the main results are new and different from the usual methods. Some suitable examples ar...

A fixed point theorem for discontinuous functions

We establish the following fixed point theorem. Let P be a non-empty polytope in the n-dimensional Euclidean space and let f be a function from P to P satisfying that for every x in P for which f(x) 6= x there exists a neighborhood of x in P such that for any y and z in this neighborhood the inner product of f(y)− y and f(z)− z is non-negative. Then there exists x∗ ∈ P satisfying f(x∗) = x∗, i....

A Fixed Point Theorem for Analytic Functions

We denote that set by A(z,w,k) and (following [1]) call it the Apollonius circle of constant k associated to the points z and w. The set A(z,w,k) is a circle for all values of k other than 1 when it is a line. In this paper, we consider z,w ∈ U, show that if z = w, then necessarily A(z,w, √ (1−|w|2)/(1−|z|2)) meets the unit circle twice, consider the arc on the unit circle with those endpoints,...

Vector ultrametric spaces and a fixed point theorem for correspondences

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.

A Fixed Point Theorem for Continuous Multi-valued Transformations