| Abstract: |
| We study fixed point theorems of contractive mappings in b-metric space, cone b-metric space, and the newly introduced extended b-metric space. To generalize an existence and uniqueness result for the so-called $\Phi_s$ functions in the b-metric space to the extended b-metric space and the core b-metric space, we introduced the class of $\Phi_M$ functions and applied the H\older continuous condition in the extended b-metric space. The obtained results are applied to prove existence and uniqueness of solutions and positive solutions for nonlinear integral equations and fractional boundary value problems. Examples and numerical simulation are given to illustrate the applications. |
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