Abstract
This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument, x ( t ) = p ( t ) + x ( t ) ∫ 0 1 k ( t , τ ) ( T x ) ( τ ) d τ , where p , k are given functions, T is the given operator satisfying conditions specified later and x is an unknown function. Through the classical Schauder fixed point theorem and a new conclusion about the relative compactness in Hölder spaces, we obtain the existence of solutions under certain assumptions. Our work is more general than the previous works in the Conclusion section. At the end, we introduce several tangible examples where our entity result can be adopted.
Highlights
The work of differential equations, with an altered argument being latest, has continued for decades
Integral equations stem from several applications in specification numerous real-world problems
The purpose of this paper is to examine the existence of solutions of the following integral equation of the Fredholm type with a changed argument, x (t) = p(t) + x (t)
Summary
The work of differential equations, with an altered argument being latest, has continued for decades. For more data and consequences related to these equations, see [1,2,3] These topics have linear modifications of their arguments and have been worked on by the authors in the papers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The purpose of this paper is to examine the existence of solutions of the following integral equation of the Fredholm type with a changed argument, x (t) = p(t) + x (t). Schauder fixed point theorem and the relative compactness in Hölder spaces
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