Dissertation•
Fixed Points for Multivalued Mappings and the Metric Completeness = จุดตรึงสำหรับการส่งหลายค่าและความบริบูรณ์เชิงเมตริก / Hatairat Yingtaweesittikul
01 Jan 2010-
TL;DR: In this paper, the equivalence of the existence of fixed points of single-valued mappings and multivalued mappings for some classes of mappings was studied and some equivalence theorems for the completeness of metric spaces were proved.
Abstract: We consider the equivalence of the existence of fixed points of single-valued mappings and multivalued mappings for some classes of mappings by proving some equivalence theorems for the completeness of metric spaces.
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TL;DR: In this article, the authors extend the celebrated result of W. A. Kirk that a metric space is complete if and only if every Caristi self-mapping for has a fixed point, to partial metric spaces.
Abstract: We extend the celebrated result of W. A. Kirk that a metric space is complete if and only if every Caristi self-mapping for has a fixed point, to partial metric spaces.
243 citations
TL;DR: In this article, the fixed point theorems for set-valued mappings in the context of b-metric spaces were established and generalized to the case of fixed point spaces.
Abstract: The aim of this paper is to establish some fixed point theorems for set-valued mappings in the context of b-metric spaces. The proposed theorems expand and generalize several well-known comparable results in the literature. An example is also given to support our main result. MSC: 46S40, 47H10, 54H25.
48 citations
TL;DR: In this paper, the existence of a common solution for certain class of functional equations arising in dynamic programming, under much weaker conditions, is discussed. And the results obtained here in generalize many well known results.
Abstract: Coincidence and fixed point theorems for a new class of hybrid contractions consisting of a pair of single-valued and multivalued maps on an arbitrary nonempty set with values in a metric space are proved. In addition, the existence of a common solution for certain class of functional equations arising in dynamic programming, under much weaker conditions are discussed. The results obtained here in generalize many well known results.
35 citations
TL;DR: The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of Đoric and Lazovic (2011) for a multivaluing map on a metric space satisfying Ciric-Suzuki-type-generalized contraction.
Abstract: The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of Đoric and Lazovic (2011) for a multivalued map on a metric space satisfying Ciric-Suzuki-type-generalized contraction. Further, as a special case, we obtain a generalization of an important common fixed point theorem of Ciric (1974). Existence of a common solution for a class of functional equations arising in dynamic programming is also discussed.
32 citations
TL;DR: In this article, a new type of multivalued operators similar to those of the Kikkawa-Suzuki type was introduced and some basic problems of the fixed point and strict fixed point for them were presented.
Abstract: The aim of this paper is to introduce a new type of multivalued operators similar to those of Kikkawa–Suzuki type and to present some basic problems of the fixed point and strict fixed point for them. Obtained results generalize, complement and extend classical results given by Ciric [Lj.B. Ciric, Fixed points for generalized multi-valued contractions, Mat. Vesnik 9 (24) (1972) 265–272] or Nadler [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475–488], as well as recent results given by Kikkawa and Suzuki [M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008) 2942–2949], Moţ and Petrusel [G. Moţ, A. Petrusel, Fixed point theory for a new type of contractive multivalued operators, Nonlinear Anal. 70 (2009) 3371–3377]. Applications to certain functional equations arising in dynamic programming are also considered.
28 citations
Cites background from "Fixed Points for Multivalued Mappin..."
...Then there exists z ∈ X such that z ∈ T z. Theorem 1.6 has further been generalized by Dhompongsa and Yingtaweesittikul [7], Dorić and Lazović [8], Moţ and Petruşel [15], and Singh and Mishra [28]....
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...6 has further been generalized by Dhompongsa and Yingtaweesittikul [7], Dorić and Lazović [8], Moţ and Petruşel [15], and Singh and Mishra [28]....
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3,349 citations
04 Feb 2002
TL;DR: In this paper, a probabilistic approach is presented to prove blow-up of solutions of the Fujita equation ∆w/∂t = -(-Δ) α/2 w + w 1+β in the critical dimension d = α/β.
Abstract: We present a probabilistic approach which proves blow-up of solutions of the Fujita equation ∂w/∂t = -(-Δ) α/2 w + w 1+β in the critical dimension d = α/β. By using the Feynman-Kac representation twice, we construct a subsolution which locally grows to infinity as t → ∞. In this way, we cover results proved earlier by analytic methods. Our method also applies to extend a blow-up result for systems proved for the Laplacian case by Escobedo and Levine (1995) to the case of α-Laplacians with possibly different parameters a.
1,130 citations
TL;DR: Some results on fixed points were discussed in this article, where the authors proposed a method for computing fixed points in a fixed point set, using fixed points as the fixed point function.
Abstract: (1969). Some Results on Fixed Points—II. The American Mathematical Monthly: Vol. 76, No. 4, pp. 405-408.
519 citations
06 Dec 2007
TL;DR: The Meir-Keeler fixed point theorem as discussed by the authors is a simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space, and it can be seen as a special case of the fixed-point theorem.
Abstract: We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space. We also discuss the Meir-Keeler fixed point theorem.
435 citations