Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

Abstract

In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

On tripled fixed point theorems via measure of noncompactness with applications to a system of fractional integral equations

“…Using the above two modified class of control functions, we prove the following results. In fact, we omitted some conditions on control functions ω and ϑ than the above classes introduced in [21] and [22].…”

“…This function is not an element of Ω. Also, ϑ is not a function in collection Θ introduced in [22]. So, we have larger collections of functions with respect to the classes of functions introduced in [22].…”

“…In [22], the authors extended Darbo's fixed point theorem using the concept of ϑ-ω-contractions. From now on, a nonempty, bounded, closed and convex subset Π of a Banach space B is indicated by NBCC, shortly.…”

Calendar Effect and In-Sample Forecasting Applied to Mesothelioma Mortality Data

“…Reference [37] proved the existence of a unique solution for the above empirical equations (see also [41] for related theoretical tools); however, the solution cannot be explicitly obtained, and a backfitting algorithm is required in practice to derive estimateŝ f 1 ,f 2 andf 3 . The algorithm can be written as follows.…”

On solution of generalized proportional fractional integral via a new fixed point theorem

“…Hence, cf (X ) = 1 (X 1 ) + 2 (X 2 ) is an MNC in the space E × E, where X t , t = 1, 2, denotes the natural projections of X . Definition 2.10 ( [30]) Suppose that G is the set of all functions μ : R + → R satisfying the following conditions:…”