Open AccessFixed point theorems for countably asymptotically Ф-nonexpansive maps in locally convex spaces and application
Author(s) -
Afif Ben Amar,
Salma Derbel
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2003879b
Subject(s) - mathematics , regular polygon , fixed point , fixed point theorem , locally convex topological vector space , schauder fixed point theorem , pure mathematics , uniformly convex space , type (biology) , discrete mathematics , mathematical analysis , banach space , lp space , brouwer fixed point theorem , geometry , ecology , banach manifold , biology
In this paper, we introduce the concept of a countably asymptotically ?-nonexpansive operator. In addition, we establish new fixed point results for some countably asymptotically ?-nonexpansive and sequentially continuous maps, fixed-point results of Krasnosel?skii type in locally convex spaces. Moreover, we present Leray-Schauder-type fixed point theorems for countably asymptotically ?-nonexpansive maps in locally convex spaces. Apart from that we show the applicability of our results to the theory of Volterra integral equations in locally convex spaces. The main condition in our results is formulated in terms of the axiomatic measure of noncompactness. Our results improve and extend in a broad sense recent ones obtained in literature.