In this paper, we introduce a new concept of locally $ \alpha $-$ \psi $-contractive mapping, generalized $ \alpha-\psi $ rational contraction and establish fixed point theorems for such mappings in the setting of extended $ b $-metric space. Our main results extend and improve some results given by some authors. We also provide a non trivial example to show the validity of our main results. As an application, we derive some new fixed point result for $ \psi $-graphic contraction defined on an extended $ b $-metric space endowed with a graph.
Citation: Afrah A. N. Abdou, Maryam F. S. Alasmari. Fixed point theorems for generalized $ \alpha $-$ \psi $-contractive mappings in extended $ b $-metric spaces with applications[J]. AIMS Mathematics, 2021, 6(6): 5465-5478. doi: 10.3934/math.2021323
In this paper, we introduce a new concept of locally $ \alpha $-$ \psi $-contractive mapping, generalized $ \alpha-\psi $ rational contraction and establish fixed point theorems for such mappings in the setting of extended $ b $-metric space. Our main results extend and improve some results given by some authors. We also provide a non trivial example to show the validity of our main results. As an application, we derive some new fixed point result for $ \psi $-graphic contraction defined on an extended $ b $-metric space endowed with a graph.
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Afrah A. N. Abdou, Maryam F. S. Alasmari. Fixed point theorems for generalized $ \alpha $-$ \psi $-contractive mappings in extended $ b $-metric spaces with applications[J]. AIMS Mathematics, 2021, 6(6): 5465-5478. doi: 10.3934/math.2021323
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