We introduce a Ćirić type contraction principle in a vector-valued $ b $-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings $ W, E:G\rightarrow G $ ($ G $ is a non-empty set), for which these mappings admit a unique common fixed point in $ G $ subject to a nonlinear operator $ {\bf F}:\mathbb{P}^{m} \rightarrow \mathbb{R}^{m} $. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integro-differential equations and apply the obtained fixed point theorem to show the existence of a solution to this model.
Citation: Muhammad Nazam, Aftab Hussain, Asim Asiri. On a common fixed point theorem in vector-valued $ b $-metric spaces: Its consequences and application[J]. AIMS Mathematics, 2023, 8(11): 26021-26044. doi: 10.3934/math.20231326
We introduce a Ćirić type contraction principle in a vector-valued $ b $-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings $ W, E:G\rightarrow G $ ($ G $ is a non-empty set), for which these mappings admit a unique common fixed point in $ G $ subject to a nonlinear operator $ {\bf F}:\mathbb{P}^{m} \rightarrow \mathbb{R}^{m} $. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integro-differential equations and apply the obtained fixed point theorem to show the existence of a solution to this model.
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Muhammad Nazam, Aftab Hussain, Asim Asiri. On a common fixed point theorem in vector-valued $ b $-metric spaces: Its consequences and application[J]. AIMS Mathematics, 2023, 8(11): 26021-26044. doi: 10.3934/math.20231326
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