Topic
Coincidence point
About: Coincidence point is a research topic. Over the lifetime, 3597 publications have been published within this topic receiving 67646 citations.
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Book•
01 Jan 1977
TL;DR: In this article, a generalized continuation theorem and existence theorems for Lx = Nx are given for perturbations of linear Fredholm mappings of nonzero index.
Abstract: Alternative problems : An historical perspective.- Coincidence degree for perturbations of Fredholm mappings.- A generalized continuation theorem and existence theorems for Lx = Nx.- Two-point boundary value problems : Nonlinearities without special structure.- Approximation of solutions - The projection method.- Quasibounded perturbations of Fredholm mappings.- Boundary-value problems for some semilinear elliptic partial differential equations.- Periodic solutions of ordinary differential equations with quasibounded nonlinearities and of functional differential equations.- Coincidence index, multiplicity and bifurcation theory.- Coincidence degree for k-set contractive perturbations of linear Fredholm mappings.- Nonlinear perturbations of fredholm mappings of nonzero index.
1,538 citations
Book•
28 Sep 1990TL;DR: In this paper, the basic fixed point theorems for non-pansive mappings are discussed and weak sequential approximations are proposed for linear mappings with normal structure and smoothness.
Abstract: Introduction 1. Preliminaries 2. Banach's contraction principle 3. Nonexpansive mappings: introduction 4. The basic fixed point theorems for nonexpansive mappings 5. Scaling the convexity of the unit ball 6. The modulus of convexity and normal structure 7. Normal structure and smoothness 8. Conditions involving compactness 9. Sequential approximation techniques 10. Weak sequential approximations 11. Properties of fixed point sets and minimal sets 12. Special properties of Hilbert space 13. Applications to accretivity 14. Nonstandard methods 15. Set-valued mappings 16. Uniformly Lipschitzian mappings 17. Rotative mappings 18. The theorems of Brouwer and Schauder 19. Lipschitzian mappings 20. Minimal displacement 21. The retraction problem References.
1,466 citations
TL;DR: In this paper, a common fixed point theorem of S.L. and S.P. Singh is generalized by weakening commutativity hypotheses and by increasing the number of functions involved.
Abstract: A common fixed point theorem of S.L. and S.P. Singh is generalized by weakening commutativity hypotheses and by increasing the number of functions involved.
1,249 citations
TL;DR: In this paper, a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order was proved, using a weak contractivity type of assumption, which can be used to investigate a large class of problems.
Abstract: We prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order, using a weak contractivity type of assumption. Besides including several recent developments, our theorem can be used to investigate a large class of problems. As an application, we discuss the existence and uniqueness of solution for a periodic boundary value problem.
1,206 citations