This paper discusses some existence results for at least one continuous solution for generalized fractional quadratic functional integral equations. Some results on nonlinear functional analysis including Schauder fixed point theorem are applied to establish the existence result for proposed equations. We improve and extend the literature by incorporated some well-known and commonly cited results as special cases in this topic. Further, we prove the existence of maximal and minimal solutions for these equations.
In this paper, we prove theorems on the existence of solutions in Lp(R+), 1 ? p < ?, for some functional integral equations. The basic tool used in the
proof is the fixed point theorem due to Darbo with respect to so called
measure of noncompactness. The obtained results generalize and extend
several ones obtained earlier in many papers and monographs. An example
which shows the applicability of our results is also included.
We propose a new notion of contraction mappings for two class of functions
involving measure of noncompactness in Banach space. In this regard we
present some theory and results on the existence of tripled fixed points and
some basic Darbo?s type fixed points for a class of operators in Banach
spaces. Also as an application we discuss the existence of solutions for a
general system of nonlinear functional integral equations which satisfy in
new certain conditions. Further we give an example to verify the
effectiveness and applicability of our results.
<abstract><p>Using the method of Petryshyn's fixed point theorem in Banach algebra, we investigate the existence of solutions for functional integral equations, which involves as specific cases many functional integral equations that appear in different branches of non-linear analysis and their applications. Finally, we recall some particular cases and examples to validate the applicability of our study.</p></abstract>
In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable
The aim of this paper is to investigate the solvability of infinite systems of nonlinear functional integral equations of [Formula: see text]-variables in [Formula: see text] by using the Hausdorff measure of noncompactness with the help of Meir–Keeler condensing operators. We also provide an illustrative example in support of our existence theorems.