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P-cyclic c-contraction result in Menger spaces using a control function

Choudhury B. S., Bhandari S. K.

Demonstratio Mathematica

2016

Vol. 49, nr 2

213--223

The intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways, one of which being the C-contraction. Cyclic contractions are another type of contractions used extensively in global optimization problems. We introduced here p-cyclic contractions which are probabilistic C-contraction types. It involves p numbers of subsets of the spaces and involves two control functions for its definitions. We show that such contractions have fixed points in a complete probabilistic metric space. The main result is supported with an example and extends several existing results.

A Kannan-like contraction in partially ordered spaces

Choudhury B.S., Kundu A.

Demonstratio Mathematica

2013

Vol. 46, nr 2

327--334

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.