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A fixed point theorem in reflexive Banach Spaces
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A Generalized Banach Fixed Point Theorem
Bulletin of the Malaysian Mathematical Sciences Society, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shukla, Satish +2 more
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A fixed point theorem in reflexive Banach spaces
Mathematics Seminar Notes, 1983In a recent paper \textit{J.-C. Hwang} and \textit{M.-H. Shih} [Commentari Math. Univ. St. Pauli 25 (1976), 95-96 (1977; Zbl 0366.47025)] proved a fixed point theorem. The proof therein is rather long and computational. In this note, we present a short proof of a more general result, namely Theorem 1.
Sehgal, V. M., Singh, S. P.
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2–Cone Banach spaces and fixed point theorem
AIP Conference Proceedings, 2012The present article deals with 2–cone normed spaces, 2–cone Banach spaces. Also, some results expressing under what conditions a self-mapping T of 2–cone Banach space (X, ‖.,.‖c) has a unique fixed point are given.
ŞAHİNER, Ahmet, YİĞİT, Tuba
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On Fixed Points and Multiparameter Ergodic Theorems in Banach Lattices
Canadian Journal of Mathematics, 1988We present here multiparameter results about positive operators acting on a weakly sequentially complete Banach lattice. Sections 1, 2 and 3 generalize results obtained by M. A. Akcoglu and the second author in the case of a contraction. Even in that case, the classical L1 theory extends to Banach lattices only under an additional monotonicity ...
Millet, Annie, Sucheston, Louis
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Some Fixed Point Theorems in Metric and Banach Spaces
Canadian Mathematical Bulletin, 1969The purpose of this paper is two-fold. Sections 2 and 3 are motivated by an observation that certain theorems concerning "diminishing orbital diameters" (introduced in [1]) are true under weaker assumptions. Specifically, we investigate the relationship between that concept and alternate conditions such as "asymptotic regularity", and in the process we
Belluce, L. P., Kirk, W. A.
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The Banach Fixed Point Theorem
2013This chapter is devoted to the Banach fixed point theorem and some of its immediate consequences. In particular, we shall prove the usual version of the implicit function theorem in Banach spaces and present some applications to boundary value problems. This requires knowing the basic notions of differentiation in Banach spaces, which, for the reader’s
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Banach's Fixed-Point Theorem as a base for data-type equations
Applied Categorical Structures, 1994The paper develops a theory of data types in categories enriched by CMS (complete metric spaces) analogous to the theory in categories enriched by CPO (complete posets). In this case for a category \({\mathcal K}\) of data types solutions of recursive data-type equations \(X\cong T(X)\), where \(T:{\mathcal K}\to{\mathcal K}\) is a locally continuous ...
Jirí Adámek, Jan Reiterman
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Fixed point theorem for -nonexpansive mappings in Banach spaces
Nonlinear Analysis: Theory, Methods & Applications, 2011The concept of \(\alpha\)-nonexpansive mapping in a Banach space is introduced and some generalizations of previous theorems from Hilbert to Banach spaces are given. Definition. Let \(E\) be a Banach space and \(C\subset E\).
Aoyama, Koji, Kohsaka, Fumiaki
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Banach Contraction Fixed Point Theorem
2018The main goal of this chapter is to introduce notion of distance between two points in an abstract set. This concept was studied by M. Frechet and it is known as metric. Existence of a fixed point of a mapping on a complete metric into itself was proved by S. Banach around 1920.
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