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1.
Abstract The main purpose of this article is to prove a collection of new nxea point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for (ws)-compact (in particular nonexpansive) self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations. 相似文献
2.
Afif Ben Amar Donal O’Regan Amel Touati 《Journal of Fixed Point Theory and Applications》2016,18(4):771-784
In this paper, we introduce the concept of an asymptotically \({\Phi}\)-nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically \({\Phi}\)-nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings. 相似文献
3.
Afif Ben Amar 《Central European Journal of Mathematics》2011,9(4):851-865
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder
type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary
value problem arising in the theory of growing cell population in L
1-setting. Besides, a topological structure of the set of solutions is provided. 相似文献
4.
Shaoyuan Xu 《分析论及其应用》2007,23(3):274-282
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem, Petryshyn's theorem, etc. 相似文献
5.
Afif Ben Amar 《Central European Journal of Mathematics》2013,11(1):85-93
The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. 相似文献
6.
Afif Ben Amar 《Journal of Functional Analysis》2010,259(9):2215-2237
We introduce a class of Banach algebras satisfying certain sequential condition (P) and we prove fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators. Later on, we give some examples of applications of these types of results to the existence of solutions of nonlinear integral equations in Banach algebras. 相似文献
7.
The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear
operator equation F(x) =αx (α ≥ 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept
of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for
the nonlinear operator equation F(x) = αx (α ≥ 1) for such class of operators. As consequences, the main results generalize and improve the relevant results, which are
obtained by O’Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point
theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive
(μ-nonexpansive) and weakly semi-closed operators at the origin and their generalizations. The main condition in our results
is formulated in terms of axiomatic measures of weak compactness. 相似文献
8.
The main purpose of this paper is to prove a collection of new fixed point theorems for so-called weakly F-contractive mappings. By analogy, we introduce also a class of strongly F-expansive mappings and we prove fixed point theorems for such mappings. We provide a few examples, which illustrate these results and, as an application, we prove an existence and uniqueness theorem for the generalized Fredholm integral equation of the second kind. Finally, in Appendix A, we apply the Mönch fixed point theorem to prove two results on the existence of approximate fixed points of some continuous mappings. 相似文献
9.
Motivated by the study of a general radiative transfer problem, we state some new variants of Leray–Schauder type fixed point theorems for weakly sequentially continuous operators. Further, we apply our results to establish some new existence and locality principles for a source problem in L1‐setting with generally boundary conditions. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
In this article, we prove some fixed point theorems of Leray-Schauder Type in Banach Algebra satisfying certain sequential condition (𝒫) for the sum and the product of nonlinear weakly sequentially continuous operators and we give an example of application to a functional nonlinear integral equation. 相似文献
11.
Shihuang Hong 《Journal of Mathematical Analysis and Applications》2008,337(1):333-342
In this paper, the existence and iterative approximation of fixed points for a class of systems of mixed monotone multivalued operator are discussed. We present some new fixed point theorems of mixed monotone operators and increasing operators which need not be continuous or satisfy a compactness condition. We also give some applications to differential inclusions with discontinuous right hand side in Banach spaces and to Hammerstein integral inclusions on RN. 相似文献
12.
Meiyu Zhang 《Journal of Mathematical Analysis and Applications》2008,339(2):970-981
In this paper, ? convex −ψ concave mixed monotone operators are introduced and some new existence and uniqueness theorems of fixed points for mixed monotone operators with such convexity concavity are obtained. As an application, we give one example to illustrate our results. 相似文献
13.
Sehie Park 《Journal of Mathematical Analysis and Applications》2007,329(1):690-702
We obtain new fixed point theorems on multimaps in the class Bp defined on almost convex subsets of topological vector spaces. Our main results are applied to deduce various fixed point theorems, coincidence theorems, almost fixed point theorems, intersection theorems, and minimax theorems. Consequently, our new results generalize well-known works of Kakutani, Fan, Browder, Himmelberg, Lassonde, and others. 相似文献
14.
In this paper, φ concave-(−ψ) convex operators are introduced and some new existence and uniqueness theorems of fixed points of mixed monotone operators with such concavity and convexity are obtained. Moreover, some applications to nonlinear integral equations on bounded or unbounded regions are given. 相似文献
15.
Rafael Espínola Adrian Petru?el 《Journal of Mathematical Analysis and Applications》2005,309(2):420-432
The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petru?el, and Sînt?m?rian [I.A. Rus, A. Petru?el, A. Sînt?m?rian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959]. 相似文献
16.
We characterize the p-approximation property (p-AP) introduced by Sinha and Karn [D.P. Sinha, A.K. Karn, Compact operators whose adjoints factor through subspaces of ?p, Studia Math. 150 (2002) 17-33] in terms of density of finite rank operators in the spaces of p-compact and of adjoints of p-summable operators. As application, the p-AP of dual Banach spaces is characterized via density of finite rank operators in the space of quasi-p-nuclear operators. This relates the p-AP to Saphar's approximation property APp′. As another application, the p-AP is characterized via a trace condition, allowing to define the trace functional on certain subspaces of the space of nuclear operators. 相似文献
17.
Xie Ping Ding 《Journal of Mathematical Analysis and Applications》2002,266(1):21-37
Some new generalized G-KKM and generalized S-KKM theorems are proved under the noncompact setting of generalized convex spaces. As applications, some new minimax inequalities, saddle point theorems, a coincidence theorem, and a fixed point theorem are given in generalized convex spaces. These theorems improve and generalize many important known results in recent literature. 相似文献
18.
S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i(A,Ω, p) is equal to nonzero, where i(A,Ω, p) is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point the-orems of the completely continuous and weakly inward mapping, which generalize... 相似文献
19.
Nikita Szidorov 《Acta Mathematica Hungarica》2003,98(4):345-355
The aim of this paper is to prove some fixed point theorems which generalize well known basic fixed point principles of nonlinear
functional analysis. Moreover, we investigate the class of mappings f: X→ X, where X is a Banach space, for which one of the main conditions in the metric fixed point theory, namely the condition (1), is satisfied.
We obtain essential applications of this fact. All our results are illustrated by suitable examples.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces. 相似文献