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Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

Dhagat, Vanita Ben, Sharma, Akshay (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54H25, 47H10.The concept of semi compatibility is given in probabilistic metric space and it has been applied to prove the existence of unique common fixed point of four self-maps with weak compatibility satisfying an implicit relation. At the end we provide examples in support of the result.Authors thank to MPCOST, Bhopal for financial support through the project M-19/2006.

Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings

Zeqing Liu, Ravi P. Agarwal, Chi Feng, Shin Min Kang (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results are sharp....

Weak uniform normal structure and iterative fixed points of nonexpansive mappings

T. Domínguez Benavides, G. López Acedo, Hong Xu (1995)

Colloquium Mathematicae

This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with...

Weak uniform normal structure in direct sum spaces

Tomás Domínguez Benavides (1992)

Studia Mathematica

The weak normal structure coefficient WCS(X) is computed or bounded when X is a finite or infinite direct sum of reflexive Banach spaces with a monotone norm.

Weakly Picard mappings

Ioan A. Rus (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper we generalize the well known converse to the contraction principle due to C. Bessaga, dropping the uniqueness of the fixed point from its hypotheses. Some properties of weakly Picard mappings are given.

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