New fixed point theorems on b-metric spaces with applications to coupled fixed point theory

Let (X, d) be a complete b-metric space endowed with a partial order relation and f:X→X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:X\rightarrow X$$\end{document} be a Ćirić type operator. In this paper, an extended study of the fixed point equation x=f(x),x∈X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=f(x), \ x\in X$$\end{document}, is considered. As an application, coupled fixed point results are given in the same framework. Our results generalize some recent theorems in the literature.