Common fixed points of a pair of H^beta-Hausdorff multivalued operators in b-metric space and application to integral equations

Naif R Alrashedi, Fahad S Alshammari, Reny George

Abstract


A common fixed point theorem for a pair of $H^{\beta}$-Hausdorff multi-valued operators for $\beta \in [0,1]$  is proved in a  b-metric space. Our result is a proper extension and  new variants  of many well known  contraction conditions existing in literature . As an application of our main result, we have proved an existence result for a unique common common solution of a pair of Fredholm integral equations.

Keywords


b-metric space, H^beta-Hausdorff b-metric, H^beta-Hausdorff function,common fixed point, Fredholm integral equation

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