Nonlinear contractions in partially ordered quasi $b$-metric spaces
Commun. Korean Math. Soc. 2012 Vol. 27, No. 1, 117-128
Printed March 1, 2012
Masood Hussain Shah and Nawab Hussain
Department of Mathematical Sciences, King Abdulaziz University
Abstract : Using the concept of a $g$-monotone mapping we prove some common fixed point theorems for $g$-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi $b$-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [$Monotone$ $generalized$ $nonlinear$ $contractions$ $in$ $partailly$ $ordered$ $metric$ $spaces$, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [$Generalized$ $contractions$ $in$ $partially$ $ordered$ $metric$ $spaces$, Appl. Anal. $\bf 87$ (2008), 1--8].
Keywords : $g$-monotone mapping, $g$-non-decreasing mapping, coincidence, fixed point, common fixed point, complete quasi $b$-metric space
MSC numbers : Primary 54H25; Secondary 47H10
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