A Comprehensive Review Note on Pachpatte-Type Inequality
Keywords:
Convex functions, Preinvex functions, Pachpatte type inequal-ity, cr-convex functionAbstract
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.
References
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