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...

Winding numbers are fundamental objects arising in algebraic topology, with many applications in non-constructive complex analysis. We present a formalization in Coq of the winding numbers and their main properties. As an application of this development, we also give non-constructive proofs of the following theorems: the Fundamental Theorem of Algebra, the 2-dimensional Brouwer Fixed-Point theo...

In hyperconvex metric spaces, we introduce Knaster-KuratowskiMazurkiewicz mappings (in short KKM-maps). Then we prove an analogue to Ky Fan fixed point theorem in hyperconvex metric spaces.

In 1957 Ky Fan gave in [5] a necessary and sufficient condition, known as Fan’s Consistency Condition, for a finite system of convex inequalities to have a solution. This result has been somewhat overshadowed by the famous Fan’s Inequality which is equivalent to Brouwer’s Fixed Point Theorem. Another result which bears Fan’s name, but which is not due to him, is Fan’s Lopsided Inequality which ...

In this Paper we will investigate some fixed point and common theorem for multivalued mappings of Banach space. We show that an extended form many Known results taking inequities. The general a result proved by Space Convergence in which contains new generalized Theorem.