본문 바로가기
KERD
논문KCI 등재

Fixed points of weakly inward 1-set-contraction mappings

Huagui Duan|Shaoyuan Xu|Guozhen Li
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회지 (Journal of the KMS)|제45권 제6호|pp. 1725-1740

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

fixed pointfixed point indexweakly inward 1-set-contraction mapping
주제분류수학

초록

In this paper, we introduce a fixed point index of weakly inward 1-set-contraction mappings. With the aid of the new index, we obtain some new fixed point theorems, nonzero fixed point theorems and multiple positive fixed points for this class of mappings. As an application of nonzero fixed point theorems, we discuss an eigenvalue problem.

Abstract

In this paper, we introduce a fixed point index of weakly inward 1-set-contraction mappings. With the aid of the new index, we obtain some new fixed point theorems, nonzero fixed point theorems and multiple positive fixed points for this class of mappings. As an application of nonzero fixed point theorems, we discuss an eigenvalue problem.

참고문헌 (23)

  1. H. Amann, "Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces", SIAM Review, 18(4), pp.620~709 (1976)
  2. J. Caristi, "Fixed point theorems for mappings satisfying inwardness conditions", Transactions of the American Mathematical Society, 215, pp.241~251 (1976)
  3. J. Cronin, "Eigenvalues of some nonlinear operators", Journal of Mathematical Analysis and Applications, 38, pp.659~667 (1972)
  4. K. Deimling, "Nonlinear Functional Analysis" (1985), Springer-Verlag
  5. K. Deimling, "Fixed points of weakly inward multis", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 10(11), pp.1261~1262 (1986)
  6. K. Deimling, "Positive fixed points of weakly inward maps", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 12(3), pp.223~226 (1988)
  7. K. Deimling, "Fixed points of weakly inward maps in conical shells", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 12(3), pp.227~230 (1988)
  8. D. Guo, "Nonlinear Problems in Abstract Cones" (1988), Academic Press, Inc.
  9. B. Halpern, "A fixed-point theorem for inward and outward maps", Transactions of the American Mathematical Society, 130, pp.353~358 (1968)
  10. S. Hu, "Fixed points of weakly inward multivalued maps", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 10(5), pp.465~469 (1986)
  11. K. Lan, "A fixed point index for generalized inward mappings of condensing type", Transactions of the American Mathematical Society, 349(6), pp.2175~2186 (1997)
  12. K. Lan, "A fixed point index for weakly inward A-proper maps", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 28(2), pp.315~325 (1997)
  13. R. Leggett, "Multiple positive fixed points of nonlinear operators on ordered Banach spaces", Indiana University Mathematics Journal, 28(4), pp.673~688 (1979)
  14. G. Li, "The fixed-point index and the fixed-point theorems of 1-set-contraction mappings", Proc. Amer. Math. Soc., 통권 : 104, pp.1163~1170 (1988)
  15. G. Li, "Fixed point theorems of 1-set-contractive operators in Banach spaces", Applied Mathematics Letters, 19(5), pp.403~412 (2006)
  16. L. Liu, "Some random approximations and random fixed point theorems for 1-setcontractive random operators", Proc. Amer. Math. Soc., 통권 : 125, pp.515~521 (1997)
  17. L. Liu, "Approximation theorems and fixed point theorems for various classes of 1-setcontractive mappings in Banach spaces", Acta Mathematica Sinica English Series, 17(1), pp.103~112 (2001)
  18. I. Massabo, "Positive eigenvectors of k-set contractions", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 3(1), pp.35~44 (1979)
  19. W. Petryshyn, "Remarks on condensing and k-set-contractive mappings", Journal of Mathematical Analysis and Applications, 39, pp.717~741 (1972)
  20. Y. Sun, "Multiple positive fixed points of weakly inward mappings", Journal of Mathematical Analysis and Applications, 148(2), pp.431~439 (1990)
  21. J. Webb, "A-properness and fixed points of weakly inward mappings", Journal of the London Mathematical Society, 27(1), pp.141~149 (1983)
  22. S. Xu, "Fixed points for weakly inward mappings in Banach spaces", Journal of Mathematical Analysis and Applications, 319(2), pp.863~873 (2006)
  23. W. Zou, "Positive fixed point and eigenvalue results for weakly inward maps", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 27(12), pp.1447~1461 (1996)

관련 논문AI추천

Fixed point theory for inward set valued maps in hyperconvex metric spacesA. Amini-Harandi,, A. P. Farajzadeh, D. O’Regan, R. P. Agarwal영남수학회 · East Asian Mathematical Journal2008 · 제24권 제4호The Existence of Fixed Points for Generalized Weak ContractionsZhiqun Xue경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제4호Fixed point theorems for condensing mappings satisfying Leray-Schauder type conditionsShaini Pulickakunnel, Sreya Valiya Valappil대한수학회 · 대한수학회논문집2016 · 제31권 제1호Eigenvalues of countably condensing maps김연호, 김인숙, Sunghui Kwon대한수학회 · 대한수학회지2009 · 제46권 제2호Fixed points, eigenvalues and surjectivity김인숙대한수학회 · 대한수학회지2008 · 제45권 제1호Fixed point theory for various classes of permissible maps via index theoryDonal O'Regan, Ravi P. Agarwal대한수학회 · 대한수학회논문집2009 · 제24권 제2호

이 간행물의 다른 논문 (19건)

Structural stability of vector fields with orbital inverse shadowingYong Zhang, 이준희, 이건희pp. 1505-1521ANALYTIC FUNCTIONS SHARING THREE VALUES DM IN ONE ANGULAR DOMAIN이홍천, Ting-Bin Caopp. 1523-1534Multiplier theorems in weighted Smirnov spacesDaniyal M. Israfilov, Ali Guvenpp. 1535-1548MULTIPLE PERIODIC SOLUTIONS OF p-LAPLACIAN EQUATION WITH ONE-SIDE NAGUMO CONDITIONJian Jun Zhang, Tai Yong Chen, Jin Bo Ni, Wen Bin Liupp. 1549-1559Weighted estimates for certain rough singular integralsChunjie Zhangpp. 1561-1576
원문 보기