A Comprehensive Review Note on Pachpatte-Type Inequality (Global Journal of Sciences, 2024)
Convex functions have a long and illustrious history. The history of convexity theory can  be traced all the way back to the end of the nineteenth century. The word ”convex  functions” has been widely used and explored in the well-known and popular book namely  ”Inequalities,” published by G. Polya, G.H. Hardy, and J.E. Littlewood [1]. This book is  quickly became a standard reference for mathematicians and dedicated solely to the topic of  inequality and serves as an excellent introduction to this fascinating field. Convex theory  provides us with appropriate guidelines and techniques to focus on a broad range of  problems in applied sciences. It has been widely acknowledged in recent years that  mathematical inequalities have contributed to the development of various aspects of  mathematics as well as other scientific disciplines. This theory have remarkable uses in  economics [2], optimization [3], mathematical optimization for modeling [4, 5], finance  [6], computer science [7], control systems [8] and estimation and signal processing [9].  This theory provides a solid framework for the start and growth of numerical tools for  the study and solution of challenging mathematical issues. The investigation of inequality has been regarded and viewed as one of the key fields of  ap-plied sciences. It is a fast-growing science with a rising number of applications in many  scientific domains. Integral inequalities have fruitful importance in integral operator  theory, stochastic processes, numerical integration, optimization theory, probability,  statistics and information technology.
Keywords: Convex functions; Preinvex functions; Pachpatte type inequal-ity; cr-convex function