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 ...

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...

*Correspondence: [email protected] Accounting School, Zhejiang University of Finance and Economics, Hangzhou, 310018, China Abstract By using R-weak commutativity of type (Ag) and non-compatible conditions of self-mapping pairs in generalized metric space, without the conditions for the completeness of space and the continuity of mappings, we establish some new common fixed point theorems for t...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

The theorem showing that there are no non-trivial proper holomorphic self-mappings in the tetrablock is proved. We obtain also some general extension results for proper holomorphic mappings and we prove that the Shilov boundary is invariant under proper holomorphic mappings between some classes of domains containing among others (m1, . . . , mn)-balanced domains. It is also shown that the tetra...