A Comparative Study of Convexity and Quasi-Convexity

Recently, the theory of inequalities has been expanded in diverse directions to approximate the bounds of mathematical quantities. The derivation of upper bounds of error inequalities through parametric approach is an interesting problem of research. Working on that problem, we establish new analytical inequalities pertaining to convexity and quasi-convexity through a multi-parametric equation. Also, some essential deductions like trapezoid, midpoint, Bullen's and Simpson's-like inequalities will be offered to enhance existing literature. Finally, a comparison between bounds estimated through convexity and quasi-convexity is furnished. Finally, we discuss the applicable aspects of proposed inequalities to various sub-domains of analysis, including an iterative method of cubic order of convergence.