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Search Results: 1 - 10 of 288693 matches for " B. E. Rhoades "
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Two fixed-point theorems for mappings satisfying a general contractive condition of integral type
B. E. Rhoades
International Journal of Mathematics and Mathematical Sciences , 2003, DOI: 10.1155/s0161171203208024
Abstract: We establish two fixed-point theorems for mappings satisfying a general contractive inequality of integral type. These results substantially extend the theorem of Branciari (2002).
On the degree of approximation of functions belonging to the weighted $ (L^p, xi (t)) $ class by Hausdorff means
B. E. Rhoades
Tamkang Journal of Mathematics , 2001, DOI: 10.5556/j.tkjm.32.2001.305-314
Abstract: In this paper we obtain a theorem on the degree of approximation of functions belonging to a certain weighted class, using any Hausdorff method with mass function possessing a derivative. This result is a substantial generalization of the theorem of Lal [2].
On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series
B. E. Rhoades
Tamkang Journal of Mathematics , 2003, DOI: 10.5556/j.tkjm.34.2003.245-247
Abstract: In a recent paper Lal and Yadav [1] obtained a theorem on the degree of approximation for a function belonging to a Lipschitz class using a triangular matrix transform of the Fourier series representation of the function. The matrix involved was the product of $ (C, 1) $, the Cesaro matrix of order one, with $ (E, 1) $, the Euler matrix of order one. In this paper we extend this result to a much wider class of Hausdorff matrices.
On the degree of approximation of the conjugate of a function belonging to the weighted $ W(L^p, xi(t))$ class by matrix means of the conjugate series of a Fourier series
B. E. Rhoades
Tamkang Journal of Mathematics , 2002, DOI: 10.5556/j.tkjm.33.2002.365-370
Abstract: In a recent paper Lal [1] obtained a theorem on the degree of approximation of the conjugate of a function belonging to the weighted $ W(L^p, xi(t))$ class using a triangular matrix transform of the conjugate series of the Fourier series representation of the function. The matrix involved was assumed to have monotone increasing rows. We establish the same result by removing the monotonicity conditon.
A fixed point theorem for generalized metric spaces
B. E. Rhoades
International Journal of Mathematics and Mathematical Sciences , 1996, DOI: 10.1155/s0161171296000658
Abstract: In this paper we prove two fixed point theorems for the generalized metric spaces introduced by Dhage.
A common fixed point theorem for a sequence of fuzzy mappings
B. E. Rhoades
International Journal of Mathematics and Mathematical Sciences , 1995, DOI: 10.1155/s0161171295000561
Abstract: We obtain a common fixed point theorem for a sequence of fuzzy mappings, satisfying a contractive definition more general than that of Lee, Lee, Cho and Kim [2].
A fixed point theorem for non-self set-valued mappings
B. E. Rhoades
International Journal of Mathematics and Mathematical Sciences , 1997, DOI: 10.1155/s0161171297000021
Abstract: Let X be a complete, metrically convex metric space, K a closed convex subset of X, CB(X) the set of closed and bounded subsets of X. Let F:K ¢ ’CB(X) satisfying definition (1) below, with the added condition that Fx ¢ …K for each x ¢ ¢ K. Then F has a fixed point in K. This result is an extension to multivalued mappings of a result of iri [1].
Some fixed point iteration procedures
B. E. Rhoades
International Journal of Mathematics and Mathematical Sciences , 1991, DOI: 10.1155/s0161171291000017
Abstract: This paper provides a survey of iteration procedures that have been used to obtain fixed points for maps satisfying a variety of contractive conditions. The author does not claim to provide complete coverage of the literature, and admits to certain biases in the theorems that are cited herein. In spite of these shortcomings, however, this paper should be a useful reference for those persons wishing to become better acquainted with the area.
A generalization of some fixed point theorems of K. M. Ghosh
B. E. Rhoades
International Journal of Mathematics and Mathematical Sciences , 1982, DOI: 10.1155/s0161171282000192
Abstract: This note establishes the following result. Let T be a selfmap of a normed linear space E. For 0< ¢ ‰ ¤1, define T x= x+(1 ¢ ’ )Tx for each x in E. If, in addition, S=TT satisfies any contractive definition strong enough to guarantee that S has a unique fixed point u in E, and, if TT u=T Tu, then u is the unique fixed point for T.
Quadratic optimization of fixed points for a family of nonexpansive mappings in Hilbert space
B. E. Rhoades
Fixed Point Theory and Applications , 2004, DOI: 10.1155/s1687182004309046
Abstract: Given a finite family of nonexpansive self-mappings of a Hilbert space, a particular quadratic functional, and a strongly positive selfadjoint bounded linear operator, Yamada et al. defined an iteration scheme which converges to the unique minimizer of the quadratic functional over the common fixed point set of the mappings. In order to obtain their result, they needed to assume that the maps satisfy a commutative type condition. In this paper, we establish their conclusion without the assumption of any type of commutativity.
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