Reza Allahyari

A generalization of Darbo's theorem with application to the solvability of systems of integral equations

In this paper, we give an extension of Darbos fixed point theorem associated with measures of noncompactness, and present some results on the existence of coupled fixed points for a class of condensing operators in Banach spaces. Moreover, as an application, we study the problem of existence of solutions for a general system of nonlinear integral equations.

Existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness

The aim of this paper is to establish fixed point theorems for condensing operators in the Frechet spaces. In our considerations we apply the technique of measures of noncompactness in conjunction with the Tychonoff fixed point theorem. Moreover, as an application, we study the problem of the existence of solutions for infinite systems of integral equations in two variables. The results obtained extend several ones. Finally, an example is presented to show the efficiency of our results.

A generalization on weak contractions in partially ordered b-metric spaces and its application to quadratic integral equations

We introduce the notion of almost generalized (ψ,φ,L)-contractive mappings, and establish the coincidence and common fixed point results for this class of mappings in partially ordered complete b-metric spaces. Our results extend and improve several known results from the context of ordered metric spaces to the setting of ordered b-metric spaces. As an application, we prove the existence of a unique solution to a class of nonlinear quadratic integral equations.

Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on L p ( R

Let L p ( R + ) denote the space of Lebesgue integrable functions on R + with the standard norm ? x ? p = ( ? 0 ∞ | x ( t ) | p d t ) 1 p . First, we define a new measure of noncompactness on the spaces L p ( R + ) (1 ? p < ∞). In addition, we study the existence of entire solutions for a class of nonlinear functional integral equations of convolution type using Darbos fixed point theorem, which is associated with the new measure of noncompactness. We provide some examples to demonstrate that our results are applicable whereas the previous results are not.

Solvability of Systems of Integral Equations by using the Mixed Monotone Property in Partially Ordered Metric Spaces

The purpose of this work is to present some existence results of solutions for a class of systems of mixed monotone mappings in partially ordered metric spaces. The results of this work are extensions and generalizations of known coupled and tripled fixed point results. The methods of proofs used in this work, show that most of new coupled and tripled fixed point results are merely reformulation of some fixed point results in the literature. As an interesting application of our results, we discuss the existence and uniqueness of solutions for a class of systems of nonlinear integral equations. ݔ ௜ (ݐ ) = ௜ ቆݐ ,ݔ ଵ (ݐ ), … , ݔ ௡ (ݐ ),න ௜ ൫ݐ , ݏ ,ݔ ଵ (ݏ ), … ,ݔ ௡ (ݏ )൯ݏ ఉ೔ (௧ ) ௔ ቇ .