Open Access Research

Weakly isotone increasing mappings and endpoints in partially ordered metric spaces

N Hussain1, HK Nashine2, Z Kadelburg3 and Saud M Alsulami4*

Author Affiliations

1 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

2 Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur, Chhattisgarh, 492101, India

3 Faculty of Mathematics, University of Belgrade, Studentski trg 16, Beograd, 11000, Serbia

4 Department of Mathematics, King Abdulaziz University, P.O. Box 138381, Jeddah, 21323, Saudi Arabia

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Journal of Inequalities and Applications 2012, 2012:232 doi:10.1186/1029-242X-2012-232

Published: 16 October 2012

Abstract

The aim of this work is to extend the notion of weakly isotone increasing mappings to multivalued and present common endpoint theorems for <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/232/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/232/mathml/M1">View MathML</a>-weakly isotone increasing multivalued mappings satisfying generalized <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/232/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/232/mathml/M2">View MathML</a>-weak contractive as well as almost contractive inequalities in complete partially ordered metric spaces. Examples are given in support of the new results obtained.

MSC: 47H10, 54H25, 54H10.

Keywords:
endpoint; common endpoint; partial ordering; multivalued mapping; control function; weak contractive inequalities; weakly isotone increasing mappings