FIXED POINT THEOREMS FOR WIDELY MORE GENERALIZED HYBRID MAPPINGS IN METRIC SPACES, BANACH SPACES AND HILBERT SPACES

摘要

The concept of widely more generalized hybrid mapping was introduced by Kawasaki and Takahashi in the case of Hilbert spaces. We also use this definition in the cases of metric spaces and Banach spaces. It seems that a necessary condition for any (alpha, beta, gamma, delta, epsilon, zeta, eta)-widely more generalized hybrid mappings to have a fixed point is alpha + beta + gamma + delta >= 0 or alpha + 2 min{beta-gamma} + delta >= 0. In this paper we show a fixed point theorem in metric spaces. By using this result, we show fixed point theorems in Banach spaces and Hilbert spaces. Moreover our new fixed point theorems do not need the both of the assumption alpha + beta + gamma + delta >= 0 or alpha + 2 min{beta, gamma} + delta >= 0.