$\phi$-fixed point results in $b$-metric spaces with $wt$-distance

In this paper, our program is to obtain a $\phi$-fixed point result along with some applications. The problem considered here is formulated by combining together several recent trends in metric fixed point theory and its extensions. Two illustrative examples are discussed. It is shown that some results existing in the literature are extended by our main theorem. The application presented is in the area of Volterra and Fredholm integral equations.