Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function

Abstract

Trigonometric P-function is defined as a special case of h-convex function. In this article, we used a general lemma that gives trapezoidal, midpoint, Ostrowski, and Simpson type inequalities. With the help of this lemma, we have obtained many integral inequalities and generalisations for trigonometric P-function. We have shown that it goes down to the studies in special cases which are described in our study. Apart from that, we got new results for the trapezoidal, midpoint, Ostrowski, and Simpson type inequalities.

New inequalities of hermite-hadamard type for functions whose second derivatives absolute values are exponential trigonometric convex

“…Proof: The proof is make by giving the numerical results of integrals. The required result is completed which indicates that the inequality (11) gives a better result than the inequality (10).…”

“…The algebraic theoretical knowledge in his work has recently increased attention by researchers in inequality theory involving trigononometric convex functions. Some notable results and literature on the theory of inequalities for trigonometric convexity can be found, see [8][9][10][11][12] and the references therein. With the contribution of the research mentioned above, notable concepts such as exponential trigonometric, Harmonic trigonometric, geometric trigonometric convex functions have advanced as an important new class of convex functions.…”