B.E Rhoades

On generalizations of the Meir-Keeler type contraction maps

In 1969, Meir and Keeler [29] obtained a remarkable generalization of the Banach contraction principle. Since then, there have appeared a number of generalizations of their result. In 1981, the second author and Bae [33] extended the Meir-Keeler theorem to two commuting maps by adopting Jungck’s method. This influenced many authors, and, consequently, a number of new results in this line followed. Recent works of Sessa and others [46,47] contain common fixed point theorems of four maps satisfying certain contractive type conditions. In the present paper, we give a new result which encompasses most of such generalizations of the Meir-Keeler theorem. Further our result also includes many other generalizations of the Banach contraction principle. Some authors have obtained their results on 2-metric spaces. However, 2-metric versions are easily obtained from metric ones by an obvious

The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map

The convergence of Mann iteration is equivalent to the convergence of Ishikawa iterations, when T is an asymptotically nonexpansive and asymptotically pseudocontractive map.

Fixed point Ishikawa iterations

Abstract We first establish sufficient conditions on the coefficients of the Ishikawa iteration process to guarantee that, if the Ishikawa iterates of a continuous selfmap T , of the unit interval, converge, then they converge to a fixed point of T . Second we obtain sufficient conditions to guarantee that the iterations converge.

Matrix summability of Fourier series based on inclusion theorems, II

On utilise des theoremes dinclusion pour demontrer la sommabilite matricielle de series de Fourier

Fixed point iterations of generalized nonexpansive mappings

Soit K un sous-ensemble convexe borne clos dun espace de Hilbert H, T une auto-application non dilatation de K. Pour chaque point e dans K on etudie lapplication {A n e} ou A est une matrice triangulaire a entrees non negatives

Summability of double Fourier series by Nörlund methods at a point

Abstract We demonstrate sufficient conditions for a double Fourier series to be summable at each point by fairly large classes of double Norlund matrices. These results constitute substantial extensions and generalizations of related work of Y. S. Chow, K. N. Mishra, and P. L. Sharma.