Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points

Symmetry

卷:12

Pradip Debnath¹  Manuelde La Sen² 

[1] Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam 788011, India;

[2] Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, 48940 Leioa (Bizakaia), Spain;

关键词: fixed point;    asymptotically regular map;    set-valued map;    metric space;    orbitally continuous map;   

DOI  :  10.3390/sym12030411

来源: DOAJ

【 摘 要 】

The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities.

【 授权许可】

Unknown