A new class of knots with property P

Knots with Braid Index Three Have Property-p

We prove that knots with braid index three in the 3-sphere satisfy the Property P conjecture.

Property P for Knots admitting Certain Gabai Disks

We show that if a knot has a minimal spanning surface that admits certain Gabai disks, then this knot has Property P. As one of the applications we extend and simplify a recent result of Menasco and Zhang that closed 3-braid knots have Property P. Other applications are given.

Characterization of weak fixed point property for new class of set-valued nonexpansive mappings

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

A New Class of Banach Sequence Spaces

A New Property of a Class of Jacobi Polynomials

Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at x = 1 are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials.