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Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications

Tomar A., Beloul S., Sharma R., Upadhyay S.

Demonstratio Mathematica

2017

Vol. 50, nr 1

278--298

The aim of this paper is to introduce generalized condition (B) in a quasi-partial metric space acknowledging the notion of Künzi et al. [Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M., Öztürk A., Fixed point theorems on quasi-partial metric spaces, Math. Comput. Modelling, 2013, 57, 2442-2448] and to establish coincidence and common fixed point theorems for two weakly compatible pairs of self mappings. In the sequel we also answer a rmatively two open problems posed by Abbas, Babu and Alemayehu [Abbas M., Babu G. V. R., Alemayehu G. N., On common fixed points of weakly compatible mappings satisfying generalized condition (B), Filomat, 2011, 25(2), 9-19]. Further in the setting of a quasi-partial metric space, the results obtained are utilized to establish the existence and uniqueness of a solution of the integral equation and the functional equation arising in dynamic programming. Our results are also justified by explanatory examples supported with pictographic validations to demonstrate the authenticity of the postulates.

Platinum(IV) Inhibition during Hexacyanoferrate(III) Oxidation of Reducing Sugars

Pandey E., Kambo N., Upadhyay S.

Polish Journal of Chemistry

2005

Vol. 79 / nr 10

1689-1698

The kinetics of oxidation of reducing sugars viz glucose, fructose, lactose and maltose by alkaline hexacyanoferrate(III) in the presence of platinum(IV) has been studied. The kinetic data support the formation of {platinum(IV)-sugar} complexes and their resistance to react with hexacynoferrate(III). A spectrophotometric evidence for the formation of 1:1 and 1:2 complexes between platinum(IV) and reducing sugar has also been obtained