A survey of $\mathcal{C}-$class and pair upper-class functions in fixed point theory

Document Type : Review articles


1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

2 Government Degree College Thatyur (Tehri Garhwal) Uttarakhand, India

3 S. G. R. R. (P. G.) College Dehradun, India


We demonstrate  that the $\mathcal{C}-$class functions, pair $(h,f)$ upper-class functions, cone $\mathcal{C}-$class functions, $1-1-$ up-class functions, multiplicative $\mathcal{C}-$class functions, inverse$-\mathcal{C}-$class functions, $\mathcal{C}_{F}-$simulation functions, $\mathcal{C}^{*}-$class functions are powerful and fascinating weapons for the generalization, improvement, and extension of considerable conclusions obtained in the fixed point theory. Towards the end, we point out some open problems whose answers could be interesting.