Amaresh Kundu

(ψ, α, β)-weak contractions in partially ordered metric spaces

Abstract In this paper we have generalized the weak contraction principle to coincidence point and common fixed point results in partially ordered metric spaces. Our results extend some existing results. Two examples illustrating our results are given.

Tripled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

Tripled fixed points are extensions of the idea of coupled fixed points introduced in a recent paper by Berinde and Borcut, 2011. Here using a separate methodology we extend this result to a triple coincidence point theorem in partially ordered metric spaces. We have defined several concepts pertaining to our results. The main results have several corollaries and an illustrative example. The example shows that the extension proved here is actual and also the main theorem properly contains all its corollaries.

A Kannan-like contraction in partially ordered spaces

Abstract In this paper, we have introduced a generalised Kannan type contraction. It has been established that such mappings necessarily have fixed points in a complete partially ordered metric space. The fixed point is unique under some additional conditions. The result is illustrated with an example. The work is in the line of research in fixed point theory on ordered metric structures.

Some Results on Fixed Points of Weak Contractions for Non Compatible Mappings via (E.A)-Like Property

In the present work we have established common fixed point results for non compatible mappings satisfy some weak contractions in metric spaces extending the works of Pathak et al. FILOMAT 21(2):211–234, 2007, [31], Babu and Alemayehu, J. Adv. Res. Pure Math. 2(2), 89–106, 2010, [7] and others in turn. The results are based on the newly introduced (E.A) like properties and common (E.A)-like properties in metric spaces, the initial version of which was introduced by Aamri and Moutawakil in 2002.