Hui-Sheng Ding

Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces

This paper is concerned with mixed g-monotone mappings in partially ordered metric spaces. We establish several coupled coincidence and coupled common fixed point theorems, which generalize and complement some known results. Especially, our main results complement some recent results due to Lakshmikantham and Ćirić. Two examples are given to illustrate the usability of our results.Mathematics Subject Classification(2010): 47H10, 54H25.

Mild pseudo-almost periodic solutions of nonautonomous semilinear evolution equations

This paper is concerned with pseudo-almost periodic solutions for the nonautonomous semilinear parabolic evolution equation u^(t)=A(t)u(t)+f(t,u(t)),t@?R. A new existence result of mild pseudo-almost periodic solutions for the equation is obtained by using Schauders fixed point theorem.

Some properties of Stepanov-like almost automorphic functions and applications to abstract evolution equations

This article is concerned with some properties of Stepanov-like almost automorphic (S p -a.a.) functions. We establish a composition theorem about S p -a.a. functions, and with its help, study the existence and uniqueness of almost automorphic solutions for semilinear evolution equations in Banach spaces. Moreover, integration and differentiation of S p -a.a. functions are discussed. Some theorems extend earlier results.

Composition Theorems of Stepanov Almost Periodic Functions and Stepanov-Like Pseudo-Almost Periodic Functions

We establish a composition theorem of Stepanov almost periodic functions, and, with its help, a composition theorem of Stepanov-like pseudo almost periodic functions is obtained. In addition, we apply our composition theorem to study the existence and uniqueness of pseudo-almost periodic solutions to a class of abstract semilinear evolution equation in a Banach space. Our results complement a recent work due to Diagana (2008).

Common Fixed Points of Weak Contractions in Cone Metric Spaces

Results on common fixed points of mappings in cone metric spaces under weak contractive conditions (B. S. Choudhury and N. Metiya (2010)) are unified and generalized. Also, cone metric versions of some other related results on weak contractions are proved. Examples show that our results are different than the existing ones.

Meir-Keeler type contractions in partially ordered G-metric spaces

In this paper, we establish several fixed point theorems for Meir-Keeler type contractions in partially ordered G-metric spaces.MSC:46N40, 47H10, 54H25, 46T99.

A note on the existence of positive bounded solutions for an epidemic model

Abstract In this short note, we establish an existence and uniqueness theorem about a positive bounded solution for a nonlinear infinite delay integral equation, which arises in some epidemic problems. As one can see, our main result can deal with some cases, to which many previous results cannot be applied. In addition, we show that our main result can also be applied to a Lasota–Wazewska model.

Almost Automorphic Solutions to Abstract Fractional Differential Equations

A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equation , in complex Banach spaces, with Stepanov-like almost automorphic coefficients. Moreover, an application to a fractional relaxation-oscillation equation is given.

Common fixed point theorems for weakly increasing mappings on ordered orbitally complete metric spaces

In this article, we prove existence results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally complete metric spaces. We furnish suitable examples to demonstrate the validity of the hypotheses of our results.Mathematics Subject Classification (2010): 47H10; 54H25.

Weighted pseudo almost periodic functions and applications to evolution equations with delay

In this paper, we introduce a new class of vector-valued weighted pseudo almost periodic functions and present some basic properties about these new functions. Moreover, we obtain an new existence theorem of vector-valued weighted pseudo almost periodic solution to the evolution equations x^(t)=Ax(t)+f(t,xt) with delay in a Banach space X.