In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces.

The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type $\left(\beta \right)$ and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics $\left(2006\right)]$ and Sharma [Fuzzy Sets and Systems $\left(2002\right)]$. An example has been constructed in support of our main result. All the results presented in this paper are new.

In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation $U_{tt}+d{U}_t-\sigma {(x,t,U_x)}_x+aU=f(x,t,U_x,U_t,U)$ with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function $f$. The main idea of the proof relies on the compensated compactness theory.

Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom....

This paper studies the existence and the order structure of strong Berge equilibrium, a refinement of Nash equilibrium, for games with strategic complementarities à la strong Berge. It is shown that the equilibrium set is a nonempty complete lattice. Moreover, we provide a monotone comparative statics result such that the greatest and the lowest equilibria are increasing.

The notion of simultaneous reduction of pairs of matrices and linear operators to triangular forms is introduced and a survey of known material on the subject is given. Further, some open problems are pointed out throughout the text. The paper is meant to be accessible to the non-specialist and does not contain any new results or proofs.

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foiaş. Just as a contraction is related to the Szegö kernel $k_S(z,w)={(1-zw̅)}^{-1}$ for |z|,|w| < 1, by means of $(1/k_S)(T,T*)\ge 0$, we consider an arbitrary open connected domain Ω in ℂⁿ, a complete Pick kernel k on Ω and a tuple T = (T₁, ..., Tₙ) of commuting bounded operators on a complex separable Hilbert space ℋ such that (1/k)(T,T*) ≥ 0. For a complete Pick kernel the 1/k functional calculus makes sense in a beautiful...

We describe the subspaces of $S^p$ (1 ≤ p ≠ 2 < ∞) which are the range of a completely contractive projection.

In this paper, we introduce and study the notion of completely bounded ${\Lambda }_p$ sets (${\Lambda }_p^{cb}$ for short) for compact, non-abelian groups G. We characterize ${\Lambda }_p^{cb}$ sets in terms of completely bounded $L^p\left(G\right)$ multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are ${\Lambda }_p$ sets for all p < ∞, but are not ${\Lambda }_p^{cb}$ for any p ≥ 4. This is done by showing that the space of completely bounded $L^p\left(G\right)$ multipliers...

A Banach space X has the Dunford-Pettis property (DPP) provided that every weakly compact operator T from X to any Banach space Y is completely continuous (or a Dunford-Pettis operator). It is known that X has the DPP if and only if every weakly null sequence in X is a Dunford-Pettis subset of X. In this paper we give equivalent characterizations of Banach spaces X such that every weakly Cauchy sequence in X is a limited subset of X. We prove that every operator T: X → c₀ is completely continuous...