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).

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].

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.

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.

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].

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].

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.

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.

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.