Fixed point results for generalized contractive mappings involving altering distance functions on complete quasi-metric spaces and applications


Authors

Yanbin Sang - School of Science, North University of China, Taiyuan, 030051, China.


Abstract

In this paper, we introduce \(\alpha-\psi-\phi\)-Jachymski contractive mappings with generalized altering distance functions in the setting of quasi-metric spaces. Some theorems on the existence and uniqueness of fixed points for such mappings via admissible mappings are established. Utilizing above abstract results, we derive common fixed point theorem for two operators and multidimensional fixed point results for nonlinear mappings satisfying different kinds of contractive conditions on partially ordered metric spaces. Moreover, we present some examples and applications in a Fredholm integral equation and an initial value problem for partial differential equation of parabolic type.


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