Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang; Yu-Qing Chen; Yeol Je Cho; Byung-Soo Lee

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 49-54
  • ISSN: 0010-2628

Abstract

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Let P be a cone in a Hilbert space H , A : P → 2 P be an accretive mapping (equivalently, - A be a dissipative mapping) and T : P → P be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type - A + T are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in L 2 ( Ω ) .

How to cite

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Chang, Shih-sen, et al. "Fixed point theorems for nonexpansive operators with dissipative perturbations in cones." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 49-54. <http://eudml.org/doc/248266>.

@article{Chang1998,
abstract = {Let $P$ be a cone in a Hilbert space $H$, $A: P\rightarrow 2^P$ be an accretive mapping (equivalently, $-A$ be a dissipative mapping) and $T:P\rightarrow P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $-A+T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^2(\Omega )$.},
author = {Chang, Shih-sen, Chen, Yu-Qing, Cho, Yeol Je, Lee, Byung-Soo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonexpansive mapping; accretive mapping; fixed point theorem; nonlinear integral equations; nonexpansive mapping; accretive mapping; fixed point theorem; nonlinear integral equations},
language = {eng},
number = {1},
pages = {49-54},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fixed point theorems for nonexpansive operators with dissipative perturbations in cones},
url = {http://eudml.org/doc/248266},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Chang, Shih-sen
AU - Chen, Yu-Qing
AU - Cho, Yeol Je
AU - Lee, Byung-Soo
TI - Fixed point theorems for nonexpansive operators with dissipative perturbations in cones
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 49
EP - 54
AB - Let $P$ be a cone in a Hilbert space $H$, $A: P\rightarrow 2^P$ be an accretive mapping (equivalently, $-A$ be a dissipative mapping) and $T:P\rightarrow P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $-A+T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^2(\Omega )$.
LA - eng
KW - nonexpansive mapping; accretive mapping; fixed point theorem; nonlinear integral equations; nonexpansive mapping; accretive mapping; fixed point theorem; nonlinear integral equations
UR - http://eudml.org/doc/248266
ER -

References

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  2. F. E. Browder F.E., Nonlinear nonexpansive operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A 54 (1965), 1041-1044. (1965) MR0187120
  3. Browder F.E., Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Proc. Symp. Pure Math. Vol. 18, Part 2 (1976). (1976) Zbl0327.47022MR0405188
  4. Chang S.S., Fixed Point Theory with Applications, Chongqing Publishing House, Chongqing (1984). (1984) 
  5. Chen Y.Q., The fixed point index for accretive mappings with k -set contraction perturbation in cones, Internat. J. Math. and Math. Sci. 2 (1996), 287-290. (1996) MR1375990
  6. Chen Y.Q., On accretive operators in cones of Banach spaces, Nonlinear Anal. TMA 27 (1996), 1125-1135. (1996) Zbl0883.47057MR1407451
  7. Chen Y.Q., Cho Y.J., On 1 -set contraction perturbations of accretive operators in cones of Banach spaces, J. Math. Anal. Appl. 201 (1996), 966-980. (1996) Zbl0864.47027MR1400574
  8. Gatica J.A., Kirk W.A., Fixed point theorems for contraction mappings with applications to nonexpansive and pseudo-contractive mappings, Rocky Mountain J. Math. 4 (1994), 69-79. (1994) MR0331136
  9. Isac G., On an Altman type fixed point theorem on convex cones, Rocky Mountain J. Math. 2 (1995), 701-714. (1995) Zbl0868.47035MR1336557
  10. Kirk W.A., Schonberg R., Some results on pseudo-contractive mappings, Pacific J. Math. 71 (1977), 89-100. (1977) MR0487615
  11. Morales C., Pseudo-contractive mappings and the Leray-Schauder boundary condition, Comment. Math. Univ. Carolinae 20 (1979), 745-756. (1979) Zbl0429.47021MR0555187
  12. Reinermann J., Schonberg R., Some results and problems in the fixed point theory for nonexpansive and pseudo-contractive mappings in Hilbert spaces, Academic Press, S. Swaminathan ed. (1976). (1976) 

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