in this paper, a common fixed point theorem for $psi$-weakly commuting maps in l-fuzzy metric spaces is proved.

The Four Functionals Fixed Point Theorem is a generalization of the original, as well as the functional generalizations, of the Leggett–Williams Fixed Point Theorem. In the Four Functionals Fixed Point Theorem, neither the upper nor the lower boundary of the underlying set is required to map below or above the boundary in the functional sense. As an application, the existence of a positive solu...

The Lefschetz Fixed Point Theorem generalizes a collection of fixed point theorems for different topological spaces, including maps on the n-sphere and the n-disk. Although the theorem is easily written in terms of compact manifolds, in this paper we will work entirely with topological spaces that are simplicial complexes or retracts of simplicial complexes. After developing the fundamentals of...

1. INTRODUCTION. The proof of the Brouwer fixed-point Theorem based on Sperner's Lemma [S] is often presented as an elementary combi-natorial alternative to advanced proofs based on algebraic topology. See, for example, Section 6.3 of [P1]. One may ask if this proof is really based on ideas completely different from the ideas of algebraic topology (and, in particular, the ideas of Brouwer's own...

A. Abian 1] proved the following theorem: Let f be a mapping from a nite set D. Then f has a xed point if and only if D is not a union of three mutually disjoint sets A, B and C such that A \ fA] = B \ fB] = C \ fC] = ;: (The range of f is not necessarily the subset of its domain). The proof of the suuciency is by induction on the number of elements of D. A. M akowski and K. Wi sniewski 13] sho...

Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. Later, Patrice Le Calvez gave a different proof of this theorem based only on Brouwer theory and plane topology arguments [9]. These methods per...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

‎‎‎Recently Samet et al. introduced the notion of $alpha$-$psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $alpha$-$(psi,varphi)$-contractive mappings and stablish coincidence and common fixed point theorems for two mapping in complete metric spaces. We present some examples to illustrate our results. As application...

The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existe...