in the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎we also define the concept of weakly related mappings on an ordered space‎. ‎moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

In this paper the concept of compatible map in menger space has been applied to prove common fixed point theorem. A fixed point theorem for self maps has been established using the concept of compatibility of pair of self maps.

The purpose of this paper is to prove common fixed point theorem for four mappings without continuity and compatibility on intuitionistic fuzzy metric space.

The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued napping.

Let p be a saddle fixed point for an orientation-preserving surface diffeomorphism f , admitting a homoclinic point p. Let V be an open 2-cell bounded by a simple loop formed by two arcs joining p to p, lying respectively in the stable and unstable curves at p. It is shown that f |V has fixed point index ρ ∈ {1, 2} where ρ depends only on the geometry of V near p. More generally, for every n ≥ ...

This note provides an elementary short proof of the Knas t e r Kuratowski-Mazurkiewicz-Shapley ( K K M S ) Theorem based on Brouwer's fixed point theorem. The usefulness of the K K M S Theorem lies in the fact that it can be applied to prove directly Scarf's (1967) Theorem, i.e. any balanced game has a non-empty core. We also show that the K K M S Theorem and the Ga le -N ika ido -Debreu Theore...

In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contr...

This paper presents elementary combinatorial proofs of Sperner’s Lemma and discusses several non-trivial theorems to which it has been applied. Examples are the Brouwer Fixed Point Theorem, the Fundamental Theorem of Algebra, and the solution to the Cake-cutting problem.

In this paper, the concept of semi-compatibility and weak compatibility in Fuzzy metric space has been applied to prove a common fixed point theorem. We improve the result of Kumar and Pant [14] by dropping the condition of continuity of the mapping and using semi-compatibility and weak compatibility of the mappings in place of compatibility.

The significance of fixed-point theory stems from the fact that it furnishes a unified approach and constitutes an important tool in solving equations which are not necessarily linear. On the other hand, if the fixed-point equation Tx = x does not possess a solution, it is contemplated to resolve a problem of finding an element x such that x is in proximity to Tx in some sense. Best proximity p...