We de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.

We establish a xed point theorem for a certain type of nonexpanding maps in Euclidean buildings, which is inspired by a theorem of La aille in p-adic Hodge theory [7, Theorem 3.2].

We unveil new results based on measurement that guarantee the existence of unique xed points which need not be maximal. In addition, we establish that least xed points are always attractors in the topology, and then explore the consequences of these ndings in analysis. In particular, an extension of the Banach xed point theorem on compact metric spaces 3] is obtained.

<p>A Meir-Keeler type fixed point theorem for a family of mappings is proved in Menger probabilistic metric space (Menger PM-space). We establish that completeness the equivalent to property larger class includes continuous as well discontinuous mappings. In addition it, satisfying (ϵ - δ) non-expansive established.</p>

for all x, y ∈ X . Then there exists a unique fixed point x0 ∈ X of T . This theorem, called the Banach contraction principle, is a forceful tool in nonlinear analysis. This principle has many applications and is extended by several authors: Caristi [2], Edelstein [5], Ekeland [6, 7], Meir and Keeler [14], Nadler [15], and others. These theorems are also extended; see [4, 9, 10, 13, 23, 25, 26,...

In this paper, we introduce a new class of set-valued contractions and obtain a xed point theoremfor such mappings in complete metric spaces. Our main result generalizes and improves many well-known xed point theorems in the literature.

Our aim in this paper is to study the existence of solution sets and its topological structure for non-localfractional differential equations on half-line a Banach space using Riemann-Liouville definition. Themain result based Meir-Keeler fixed point theorem condensing operators combined with measure ofnon-compactness. An example given illustrate feasibility our main result.

We present a treatment for mathematical economists of three topics in the theory of xed points: (a) the Lefschetz xed point index; (b) the Lefschetz xed point theorem; (c) the theory of essential sets of xed points. Our treatment is geometric, based on elementary techniques, and largely selfcontained. In particular there is no essential reference to algebraic topology. Within the chosen scope o...