The q-symmetric analogues of Hölder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving q-symmetric integrals are used to extend some Ostrowski-type inequalities. The q-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or s-convex. Moreover, some Hermite–Hadamard inequalities for convex functions as well as for s-convex functions are also acquired with the help of q-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.

We extend some Hardy-type inequalities with general kernels to arbitrary time scales using multivariable convex functions. Some classical and new inequalities are deduced seeking applications.

This paper contains a variety of new integral inequalities for $(s,m)$-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Caputo–Fabrizio integral operators are derived for those functions whose derivatives are $(s,m)$-convex. Inequalities involving the digamma function and special means are deduced as applications.

This research focuses on Ostrowski type inequality in the form of classical Mercer inequality via ψ -Riemann–Liouville fractional integral (F-I) operators. Using the ψ -Riemann–Liouville F-I operator, we first develop and demonstrate a new generalized lemma for differentiable functions. Based on this lemma, we derive some fractional Mercer–Ostrowski type inequalities by using the convexity theory. These new findings extend and recapture previous published results. Finally, we presented applications of our work via the known special functions of real numbers such as q-digamma functions and Bessel function.

The new outcomes of the present paper are -analogues ( stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for -convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature.