Fixed point theorems for a class of nonlinear operators in Banach spaces and applications

In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results.     

Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces

In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces. Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result, we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces. Received: 10 August 2007     

Fixed point theorems in generalized Hilbert spaces

Some fundamental fixed point theorems are proved for locally convex spaces whose generating family of seminorms satisfies the parallelogram law.     

Fixed point theorems for hybrid multivalued mappings in Hilbert spaces

In this paper, we introduce a new concept of hybrid multivalued mappings in Hilbert spaces. We then prove some properties and the existence of fixed points of these mappings. Further, we prove weak and strong convergence theorems for a finite family of hybrid multivalued mappings.     

Fixed point theorems for operators on partial metric spaces

Fixed point theorems for operators of a certain type on partial metric spaces are given. Orbitally continuous operators on partial metric spaces and orbitally complete partial metric spaces are defined, and fixed point theorems for these operators are given.     

Fixed point theorems in symmetric spaces and applications to probabilistic spaces

Several fixed point theorems for symmetric spaces are proved. Then these theorems are used in symmetric PPM-space to prove and generalize Theorem 6 of [T.L. Hicks, B.E. Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Anal. 36 (1999) 331-344].     

Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems

The piecewise continuous function space is an important state space in various nonlinear problems. In this paper, we establish some new fixed point theorems for the perturbed contraction operators in piecewise continuous function spaces. Our results can be applied to various integral operators. Some previous results are improved in this literature. As applications, the existence and uniqueness of solutions of impulsive anti‐periodic boundary value problems and the Lasota–Wazewska models with delays are exhibited at last two sections. Copyright © 2013 John Wiley & Sons, Ltd.     

局部凸空间中的不动点定理及其应用

讨论了局部凸空间中推广的Leray-Schauder度的基本性质,建立了一些新的不动点定理,并给出了对局部凸空间Cauchy初值问题的应用.这些定理是Banach空间中相应结果的推广.     

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.     

Fixed point theorems of operators with ppf dependence in banach spaces

In this paper the theory of fixed point theorems of nonlinear whose domain and range are different Banach spaces are considered. Also the analogues of the Contraction Mapping Principle. Krasnoselskii's fixed point theorem and a result on the convergence of quasinonexpansive mappings are dealt with. As an application, the existence and uniqueness of solutions of differential equations with retarded argument in Banach spaces are discussed     

Fixed point theorems in partially ordered Banach spaces with applications to nonlinear fractional evolution equations

In this paper, a notion of partially Hausdorff measure of noncompactness in partially ordered Banach spaces is introduced, and some Krasnoselskii-type fixed point theorems under certain mixed conditions are proved. Some applications of the obtained fixed point theorems are given to a class of fractional hybrid evolution equations for proving the existence of mild solutions under certain monotonicity conditions. At the end, an example of the fractional parabolic equation is given to illustrate the abstract results.     

Eigenvalue problems and fixed point theorems for a class of positive nonlinear operators

We study the eigenvalue problems for a class of positive nonlinear operators defined on a cone in a Banach space. Using projective metric techniques and Schauder’s fixed-point theorem, we establish existence, uniqueness, monotonicity and continuity results for the eigensolutions. Moreover, the method leads to a result on the existence of a unique fixed point of the operator. Applications to nonlinear boundary-value problems, to differential delay equations and to matrix equations are considered.      

Fixed point theorems for mixed monotone operators and applications to integral equations

The purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions. We also present an application to integral equations.     

Banach空间中一类序压缩映射的不动点定理

在Banach空间中,利用迭代方法,研究了满足一定条件的序压缩算子的一些性质,获得了一类序压缩映射的不动点定理,证明了相应的结果,推广和改进了原有的结论,使其应用范围更加广泛.     

Fixed point theorems in uniform spaces

Fixed point theorems in a Hausdorff uniform space are proved by considering a contractive type condition for a triplet of mappings.     

Fixed point theorems in metric spaces

In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120).