We present a new proof of the version of the Shauder-Tychonov theorem provided by Coppel in Stability and Asymptotic Behavior of Differential Equations, Heath Mathematical Monographs, Boston (1965). Our alternative proof mainly relies on the Schauder fixed point theorem.

Abstract. In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green’s function, a nonlinear alternative of Leray–Schauder-type, Guo–Krasnoselskii’s fixed point theorem in a cone and the Banach...

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.

In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.

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I give short and constructive proofs of Tarski’s fixedpoint theorem, and of Zhou’s extension of Tarski’s fixed-point theorem to set-valued maps.

In this short survey, we review the current status of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. This involves an examination of several methods which are based on the so-called Collage Theorem, a simple consequence of Banach’s Fixed Point Theorem, and its extensions.

Sufficient conditions for controllability of semilinear integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.

Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in RN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations...