COUPLED FIXED POINTS OF SKEW INCREASINGOPERATORS AND APPLICATIONS

In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.

Double coupled fixed point for multi-valued mixed increasing operators in ordered Banach spaces

In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.

A Fixed Point Theorem for Multi-valued Composite Increasing Operators in Partially Ordered Spaces

In this paper,we give a fixed point theorem for multi-valued composite increasing operators,in partially ordered spaces,which generalizes the results of [1]-[3] and [5]- [8].

A Fixed Point Theorem for Multi-valued Composite Increasing Operators

In this paper,we give a fixed point theorem for multi-valued composite increasing operators, which generalizes the theorem of the paper [1] under not only multi-valued mappings but also single-valued mappings. And we generalizes the corresponding results of [2]-[5].

Existence and Uniqueness of Fixed Points for Mixed Monotone Operators with Application

In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.

EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SUPERLINEAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

A fixed point theorem for a class of β-constrictive operators and its application to the integral equation in L^1(0,∞)

Presents the fixed point theorem for a class of β constrictive increasing operators without continuity and discusses the existence of solution of the integral equation with the discontinuous term in L 1(0,∞) by using this theorem.

Fixed Point Theorems of Mixed Monotone Operators with Applications

In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.

FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS

In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.

Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces

In this work, using an analogue of Sadovskii＇s fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F（x） =μx, （μ≥1） for some weakly sequentially continuous, weakly condensing and weakly 1-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16].

APPROXIMATE CONTROLLABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND INFINITE DELAY

This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.

PERIODIC SOLUTIONS OF SCALAR NEUTRAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

This paper deals with the existence and uniqueness of periodic solutions of the following scalar neutral Volterra integro-differential equation with infinite delaywhere a, C, D, f are continuous functions, also a(t + T) = a(t), C(t + T,s + T) = C(t, s), D(t + T,s + T) = D(t, s), f(t + T) = f(t). Sufficient conditions on the existence and uniqueness of periodic solution to this equation are obtained by the contraction mapping theorem.

An analytical solution with existence and uniqueness conditions for fractional integro-differential equations

This study aims to apply the two-step Adomian decomposition method(TSADM)to find an analytical solution of integro-differential equations for fractional order without discretization/approximation with less number of iterations and reduce the computational efforts.Moreover,we have established the results for the existence and uniqueness of a solution with the help of some fixed point theorems and the Banach contraction principle.Furthermore,the method is demonstrated on different test examples arising in real life situations.It is concluded that the TSADM provides exact solution of the fractional integro-differential equations in one iteration.At the same time,the other existing methods furnish an approximate solution and require lots of computation to solve the problem applying discretization/approximation on fractional operators.

Properties for Solutions of Nonlinear Functional Difference Equations

In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR VOLTERRA INTERGO-DIFFERENTIAL EQUATIONS

This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.

Existence of positive solutions for integral boundary value problem of fractional differential equations

In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.

Existence Results on General Integrodifferential Evolution Equations in Banach Space

In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a sufficient condition for the existence of general integrodifferential evolution equations is established.