The principal motivation of this paper is to establish a new integral equality related k-Riemann Liouville fractional operator. Employing equality, we present several inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard inequality. Additionally, some novel cases the established results different kinds derived. This sums up Riemann–Liouville and Hermit...

We consider summations over digamma and polygamma functions, often with summands of the form (±1)nψ(n + p/q)/nr and (±1)nψ(m)(n + p/q)/nr, where m, p, q, and r are positive integers. We develop novel general integral representations and present explicit examples. Special cases of the sums reduce to known linear Euler sums. The sums of interest find application in quantum field theory, including...

In this study, firstly, Hermite-Hadamard type inequalities are examined for functions whose first derivative is $s$-convex in the fourth sense. addition, second Finally, some application examples including special tools and digamma presented.

in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...