Fixed Point Theorems under c-distance in Cone Metric Spaces over Banach Algebras

HUANG Huaping, DENG Guantie†

ACTA Scientiarum Naturalium Universitatis Pekinensis - - Contents -

Laboratory of Mathematics and Complex Systems (MOE), School of Mathematical Sciences, Beijing Normal University, Beijing 100875; † Corresponding author, E-mail: denggt@bnu.edu.cn

Abstract The authors obtain several theorems of the existence and uniqueness of fixed point for contractive mappings under c-distance in cone metric spaces over Banach algebras without the assumptions of normality of cones and the continuity of mappings. The results greatly improve and complement some previous results. Moreover, a supportive example to illustrate the main assertions is also given. Otherwise, by solving the problem of existence and uniqueness for an elementary equation, a significant application for the obtained results is presented. Key words cone metric space over Banach algebra; c -distance; continuity; normality; fixed point

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