Fixed points of asymptotically regular multivalued mappings

Abstract

Some results on fixed point of asymptotically regular multivalued mapping are obtained in metric spaces. The structure of common fixed points and coincidence points of a pair of compatible multivalued mappings is also discussed. Our work generalizes known results of

Coincidence Points and R-Subweakly Commuting Multivalued Maps

“…He extended the well-known Banach contraction principle to multivalued contractions. Since then this discipline has been developed further, in which many profound concepts and results were established with considerable generality; see, for example, the work of Beg and Azam [1], Itoh and Takahashi [5], Kaneko [8], Lami Dozo [9], Mizoguchi and Takahashi [11], etc., Recently, using a coincidence point theorem of Kaneko [8], Latif and Tweddle [10] proved some coincidence and common fixed point theorems for a pair of commuting single-valued and multivalued mappings defined on a weakly compact starshaped subset of a Banach space. In this paper, the validity of Latif and Tweddle's results is established for a new class of noncommuting mappings -called i?-subweakly commuting mappings (defined above).…”

A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation

“…Since the work of Nadler [18], many authors gave generalizations of contraction principle of Banach for multivalued and hybrid pair of maps (for instance [1,2,4,5,14,15,25,27,28] and reference there in). Jungck [10] introduced the concept of compatibility for a pair of self maps, which has been extended to hybrid pair of maps by Kaneko and Sessa [15] and Beg and Azam [5] when T : X → CB(X). Recently, Bouhadjera and Godet Tobie [7] introduced subsequential continuity which is weaker than the reciprocal continuity introduced by pant [19].…”

Approximation of fixed points of multifunctions in partial metric spaces

“…In metric fixed point theory, there are many existence and approximation results for fixed points of those nonexpansive mappings which are not necessarily strictly contractive. Some authors have also provided results dealing with the existence and approximation of fixed points of certain classes of contractive multifunctions [4,5,7,9,12,13]. In [12] Reich and Zaslavski introduced and studied new inexact iterative schemes for approximating fixed points of contractive and nonexpansive multifunctions.…”