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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  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
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