Geometric trigonometrically convexity and better approximations

Abstract

In this manuscript, we introduce the concept of geometric trigonometrically convex functions. We obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value is geometric trigonometrically convex. In addition, it has been proved that the results obtained with Hölder-İşcan and improved power-mean integral inequalities give a better approach than Hölder and power-mean 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.…”

Generalized n-Polynomial p-Convexity and Related Inequalities

“…Various articles published in recent years reflect the increasing interest and research efforts in this area. Some refinements, generalizations and enhancements of convex functions and inequality (2) can be found in recent papers [14][15][16][17][18][19][20][21][22][23]. These examples highlight the growing interest and importance of generalizing convex functions and related inequalities in contemporary mathematical research.…”

Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

“…For further details and proofs on both AH convex functions and other kinds of convexity, we refer the reader to [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and references there in. To derive main results for AH convex functions, we need the following Lemma 1.5.…”