In this paper we present a selection of fixed point theorems with applications in nonlinear analysis. We begin with the Banach fixed point theorem, which we use to prove the inverse and implicit mapping theorems and the Picard-Lindelöf theorem for Banach spaces. We then prove in succession the fixed point theorems of Brouwer, Schauder, and Schaeffer, after which we conclude with two example app...

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.

and Applied Analysis 3 for 0 ≤ i ≤ n − 1, where α > 0 and β > 1 are given constants. On the one hand, the author established criteria for the existence of at least one solution and of at least one positive solution for the BVP 1.6 by using the Schauder fixed point theorem and Krasnosel’skii fixed point theorem, respectively. On the other hand, the author investigated the existence of multiple p...

This paper discusses the existence of solutions to antiperiodic boundary value problem for nonlinear impulsive fractional differential equations. By using Banach fixed point theorem, Schaefer fixed point theorem, and nonlinear alternative of Leray-Schauder type theorem, some existence results of solutions are obtained. An example is given to illustrate the main result.

We establish a fixed point theorem for a continuous function f : X → E, where E is a Banach space and X ⊆ E. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.

This paper presents new random fixed point theorems and random Leray–Schauder alternatives for a variety of maps (e.g., Bκ, Uκ c , KKM and PK maps). A random Kransnoselskii cone compression theorem for Uκ c maps is also given. Various random approximation theorems for the above classes are proved and as applications several random fixed point theorems are also derived.

In this article, a generalization of a Kakutani-Fan fixed point theorem for multi-valued mappings in Banach spaces is proved under weaker upper semi-continuity condition and it is further applied to derive a generalized version of Krasnoselskii’s fixed point theorem and some nonlinear alternatives of Leray-Schauder type for multi-valued closed mappings in Banach spaces. RESUMEN En este artículo...

In this paper‎, ‎the existence and uniqueness of the ‎solution of a nonlinear fully fuzzy implicit integro-differential equation‎ ‎arising in the field of fluid mechanics is investigated. ‎First,‎ an equivalency lemma ‎is ‎presented ‎by‎ which the problem understudy ‎is ‎converted‎ to ‎the‎ two different forms of integral equation depending on the kind of differentiability of the solution. Then...