Coincidence and fixed points for hybrid strict contractions

Abstract

We define the property (E.A) for single-valued and multivalued mappings and introduce the notion of T -weak commutativity for a hybrid pair (f, T ) of single-valued and multivalued maps. We obtain some coincidence and fixed point theorems for this class of maps and derive, as application, an approximation theorem.  2004 Elsevier Inc. All rights reserved.

On Common Property (E.A) for Hybrid Mappings in Gauge Spaces

“…If we set g = f and G = F in Theorem 6, we immediately get the following corollary, which improves and generalizes Theorem 1 of Aamri and El Moutawakil [1] and Theorem 3.3 of Kamran [2] .…”

“…Subsequently, this property was extended to multivalued mappings independently by Kamran [2] and Singh and Hashim [3] . Very recently, Liu, Wu and Li [4] defined the common property (E.A) in metric spaces which contains the property (E.A) for a hybrid pair of single-valued and multivalued mappings.…”

Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition

“…In recent years, several authors used these concepts to obtain coincidence point results of various classes of mappings on a metric space. For a survey of coincidence point theory, its applications, and related results, we refer to [1,4,5,10,13]. Meinardus [12] introduced the notion of invariant approximation.…”

Some common fixed point theorems for hybrid pairs of maps without the completeness assumption

“…Kamran [10], in 2004, rediscovered the notion of compatible of type (N) and named it as S-weak commutativity at a point.…”

“…Ò Ø ÓÒ 3º ( [10]) Let S : X → CB(X) and I : X → X. The map I is said to be S-weakly commuting at x ∈ X if IIx ∈ SIx.…”