Remarks on recent fixed point theorems and applications to integral equations (Q2777559)

The authors prove several fixed point theorems for four maps satisfying various contractive conditions which involve products of distances. The fixed point theorems proved do not require any of the maps to be continuous, and replace various definitions that relax the commutativity between the maps by weakly compatible. They then apply these theorems to solve certain types of nonlinear integral equations. NEWLINENEWLINENEWLINEThese fixed point theorems generalize the corresponding results in \textit{H. K. Pathak, Y. J. Cho, S. M. Kang}, and \textit{B. Madharia} [Demonstr. Math. 31, No. 3, 499-518 (1998; Zbl 0922.54036), \textit{H. K. Pathak} and \textit{M. S. Khan} [Czech. Math. J. 45, No. 4, 685-698 (1995; Zbl 0848.54030)], \textit{G. Jungck, P. P. Murthy} and \textit{Y. J. Cho} [ Math. Jap. 38, No.~2, 381-390 (1993; Zbl 0791.54059)], and \textit{H. K. Pathak, Y. J. Cho} and \textit{S. M. Kang} [ Int. J. Math. Math. Sci. 21, No. 4, 681-693 (1998; Zbl 0920.47051)].