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Metric fixed point theory for multivalued mappings

Hong-Kun Xu — 2000

Some new and recent results on the fixed point theory of multivalued contractions and nonexpansive mappings are presented. Discussions concerning Reich's problem are included. Existence of fixed points for weakly inward contractions is proved. Local contractions are also discussed. The Kirk-Massa theorem is extended to inward multivalued nonexpansive mappings. Using an inequality characteristic of uniform convexity, another proof of Lim's theorem on weakly inward multivalued nonexpansive mappings...

Weak uniform normal structure and iterative fixed points of nonexpansive mappings

T. Domínguez Benavides;  G. López Acedo;  Hong Xu — 1995

Colloquium Mathematicae

This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with...

The uniqueness of meromorphic functions ink-punctured complex plane

Hong Yan Xu;  San Yang Liu — 2017

Open Mathematics

The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).

Results on the deficiencies of some differential-difference polynomials of meromorphic functions

Xiu-Min Zheng;  Hong-Yan Xu — 2016

Open Mathematics

In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying lim sup r→+∞ T(r, f) T(r,  f ′ ) <+∞, lim sup r → + ∞ T ( r , f ) T ( r , f ' ) < + ∞ , and c be a non-zero complex constant, then δ(∞, f(z)m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c)nf′(z))≥ δ(∞, f′). We also investigate the value...

Zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu;  Cai-Feng Yi — 2010

Annales Polonici Mathematici

We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + ⋯ + a ₁ ( z ) f ' + D ( z ) f = 0 , (1) where D ( z ) = Q ₁ ( z ) e P ₁ ( z ) + Q ₂ ( z ) e P ₂ ( z ) + Q ₃ ( z ) e P ₃ ( z ) , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), a j ( z ) (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

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