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Fixed Point Theorem in Sequence of Hausdorff Left (Right) Sequentially Complete Quasi-Gauge Spaces


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1 Govt. Nehru P.G. College, Burhar, (Shahdol) M.P., India
     

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P. V. Subrahmanyam in the paper [7] has exploited the technique of Banach’s contraction principle in proving the fixed point theorem in Hausdorff left (right) sequentially complete quasi-gauge spaces. He has not only generelised the results of Chatterjea [1], Kannan [2,3], Reilly[4,5] and Singh[6], but unified their results by takeing the quasi-gauge spaces due to Reilly [4]. All these authors have only proved the fixed point theorem for a single complete metric space. In this paper I have followed the above technique in proving the fixed point for sequence of Hausdorff left (right) sequentially complete quasi-gauge spaces, by defining their Cartesian product as a set X = _i^X_i of sequences where x_(n ) 〖∈X〗_n given by the quasi-pseudo –metric p(x,y) =∑_1^ ∞(〖p_(n ) (x_(n,) y〗_(n )))/(n![1+p_(n))]) 〖x_(n ),y〗_(n ) )])

Keywords

Streaming Fluids, Walters’ Fluid, Porous Media, Effective Interfacial Tension.
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  • Chatterjea, S.K. Some fixed-points, Research Report No. 2. Centre of Advanced Study in Applied Mathematices , University of Calcutta, (1971)

  • Kannan,, R.: Some results on fixed points, Bulletin of the Calcutta Mathematical Society, 60 , (1968),pp.71-76.

  • Kannan,, R.: Some results on fixed points II, American Mathematical Monthly, 76,(1969) pp.405-408.

  • Reilly, I. L. : A Generalized Contraction Principle, Report Series No.9, University of Auckland (Newzealand), Department of Mathematics (An improved version is to appear in the Bulleting of the Australian Mathematical Society).

  • Reilly, I. L.: Quasi-Gauge Spaces, Journal of the London Mathematical Society (2) , 6, (1973), pp.481-487.

  • Singh, S.P. :Some results on fixed-point theorems, Yokohama Mathematical Journal,17, (1969), pp.61-64.

  • Subrahmanyam, P.V. : Remarks on some fixed-point, theorems related to Banach’s Contraction principle, Journal of Mathematical and Physical Sciences Volume qWWW No. 5, October 1974, pp.445-457.


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  • Fixed Point Theorem in Sequence of Hausdorff Left (Right) Sequentially Complete Quasi-Gauge Spaces

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Authors

K.P. Gupta
Govt. Nehru P.G. College, Burhar, (Shahdol) M.P., India

Abstract


P. V. Subrahmanyam in the paper [7] has exploited the technique of Banach’s contraction principle in proving the fixed point theorem in Hausdorff left (right) sequentially complete quasi-gauge spaces. He has not only generelised the results of Chatterjea [1], Kannan [2,3], Reilly[4,5] and Singh[6], but unified their results by takeing the quasi-gauge spaces due to Reilly [4]. All these authors have only proved the fixed point theorem for a single complete metric space. In this paper I have followed the above technique in proving the fixed point for sequence of Hausdorff left (right) sequentially complete quasi-gauge spaces, by defining their Cartesian product as a set X = _i^X_i of sequences where x_(n ) 〖∈X〗_n given by the quasi-pseudo –metric p(x,y) =∑_1^ ∞(〖p_(n ) (x_(n,) y〗_(n )))/(n![1+p_(n))]) 〖x_(n ),y〗_(n ) )])

Keywords


Streaming Fluids, Walters’ Fluid, Porous Media, Effective Interfacial Tension.

References