Existence Theorems on Advanced Contractions with Applications

Abstract

In this research article, by introducing a mapping $\phi$ defined on ${\left[0,\infty \right)}^4$ , with some axioms, we define two generalized contractions called $F_{H^{+}}^{\phi }$ -contractions and $\phi H_{\mathcal{P}}^{+}$ -contractions. We investigate their mutual relation and establish an existence theorem addressing $F_{H^{+}}^{\phi }$ -contractions with some applications.