Related papers: Generalized Fermat point
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.
We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
In this paper, we study the existence of common fixed points of family of multivalued mappings satisfying generalized F-contractive conditions in ordered metric spaces. These results establish some of the general common fixed point theorems…
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.
In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized $m$-gonal numbers required…
The article studies a generalization of the classical Fermat-Torricelli problem to normed spaces of arbitrary finite dimension. Necessary and sufficient conditions for the uniqueness of the solution of the Fermat-Torricelli problem for any…
The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.
This paper presents a new characterisation of the Fermat curve, according to the arrangement of Galois points.
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
The main purpose of this work is to extend the properties of multivalued transformations to the integral type transformations and to obtain the existence of fixed points under F-contraction. In addition, the results of this study were…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
In this paper we introduce FG- coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG- coupled fixed…
We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…
We introduce a new type of mappings in metric space which are three-point analogue of the well-known Chatterjea type mappings, and call them generalized Chatterjea type mappings. It is shown that such mappings can be discontinuous as is the…