An inverse spectral problem for the Sturm-Liouville operator with a singular potential from class $W_2^{-1}$ is solved by method of mappings. We prove uniqueness theorem, develop constructive algorithm solution and obtain necessary sufficient conditions solvability in self-adjoint non-self-adjoint cases.

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,...

We study the well-posedness of the fixed point problem for self-mappings of a metric space which are φ-max-contractions (see [6]).

We provide a short proof of a theorem, due to Iwaniec and Martin [9] and Iwaniec [8], on the self-improving integrability of quasiregular mappings.

In this paper, we introduce the concept of convex structure in generalized fuzzy metric spaces and proved common fixed point theorems for a pair self-mappings under sufficient contractive type conditions.

Given a finite family of nonexpansive self-mappings of a Hilbert space, a particular quadratic functional, and a strongly positive selfadjoint bounded linear operator, Yamada et al. defined an iteration scheme which converges to the unique minimizer of the quadratic functional over the common fixed point set of the mappings. In order to obtain their result, they needed to assume that the maps s...

Previously, Park et al. (2005) defined an intuitionistic fuzzy metric space and studied several fixed-point theories in this space. This paper provides definitions and describe the properties of type(β) compatible mappings, and prove some common fixed points for four self-mappings that are compatible with type(β) in an intuitionistic fuzzy metric space. This paper also presents an example of a ...

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Among all homeomorphisms f : Ω onto −→ Ω∗ between bounded doubly connected domains such that ModΩ 6 ModΩ∗ there exists, unique up to conformal authomorphisms of Ω, an energy-minimal diffeomorphism. No boundary conditions are imposed on f . Although any energyminimal diffeomorphis...