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Generalized Integral Inequalities Involving Some Special Functions with means Application
Jamshed Nasir
Abstract:
Several novel generalized integral inequalities for (ξ, s,m1)−convex functions are established in this study. Trapezoid, Bullen, and Simpson’s like inequalities for (ξ, s,m1)−convexïty were obtained as specific examples. By utilizing conventional inequalities like Hölder inequality, we have used a very traditional methodology.Improved Power-mean inequality and I can inequality. We provide a number of constraints involving special functions, such as the Ψ−Gamma(Di-gamma functions), Beta, and classical Euler-Gamma functions. Lastly, we also provide various means application.
Keywords:
convexity; (\sigma, s,m_1)-convex function; H¨older’s integral inequality; Power mean integral inequality; H¨older-? I¸scan integral inequality; Improved power-mean inequality; Beta function; Gamma function; di-gamma function.
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