Banach Journal of Mathematical Analysis

A Gregus type common fixed point theorem in normed spaces with application

Hemant Kumar Pathak and Rakesh Tiwari

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Abstract

n this paper, we introduce the notion of $\phi$-weakly compatible mapping for a pair of mappings. A fixed point theorem for two pairs of $\phi$-weakly compatible mappings satisfying a rational type contraction in a normed space is also established. Subsequently we use our result to find existence of solutions of variational inequalities.

Article information

Source
Banach J. Math. Anal., Volume 5, Number 1 (2011), 136-147.

Dates
First available in Project Euclid: 14 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1313362986

Digital Object Identifier
doi:10.15352/bjma/1313362986

Mathematical Reviews number (MathSciNet)
MR2738526

Zentralblatt MATH identifier
1226.47061

Subjects
Primary: 22-xx
Secondary: 46H05: General theory of topological algebras

Keywords
\phi-weakly compatible mappings variational inequality

Citation

Pathak, Hemant Kumar; Tiwari, Rakesh. A Gregus type common fixed point theorem in normed spaces with application. Banach J. Math. Anal. 5 (2011), no. 1, 136--147. doi:10.15352/bjma/1313362986. https://projecteuclid.org/euclid.bjma/1313362986


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References

  • S.A. Belbas and I.D. Mayergoyz, Application of fixed point methods, Numer. Math. 51 (1976), 631–654.
  • A. Bensovssan and J.L. Lions, Applications des inequations variationel en control stochastique, Dunod, Paris, 1978.
  • A. Bermon and R.J. Plemmons, Nonnegative matrices in mathematical sciences, Academic Press, New York, 1979.
  • M.L. Divicarro, B. Fisher and S. Sessa, A common fixedpoint theorem of Gregus type, Pub. Inst. Math. 34 (1984), 83–89.
  • G. Duvant and J.L. Lions, Inequalities in mechanics and physics, Springer-Verlog, Berlin, 1976.
  • G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779.
  • H.K. Pathak and R. George, A common fixed point theorem of gregus type for compatible mappings and its applications, Publ. Math. Debrecen 44 (1994), 1–9.
  • H.K. Pathak, S.M. Kang, Y.J. Cho and J.S. Jung, Gregus type common fixed point theorems for compatible mappings of type (T), Publ. Math. Debrecen 46(3-4) (1995), 85–299.
  • H.K. Pathak, S.N. Mishra and A.K. Kalinde, Common fixed point theorems with applicatios, Demonstratio Math. XXXVI(2) (2003), 413–426.
  • S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Pub. Inst. Math. (Beograd) 32(46) (1982), 149–153.
  • R.S. Verga, Matrix iterative analysis, Prentice Hall, Englewood Cliff, N.J., 1982.