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In the present paper, a new class of generalized (r; g, s, m, ϕ)-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (r; g, s, m, ϕ)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized (r; g, s, m, ϕ)-preinvex functions via Riemann-Liouville...
An n-simplex is called circumscriptible (or edge-incentric) if there is a sphere which is tangent to all its n(n + 1)/2 edges. We obtain a closed formula for the radius of the circumscribed sphere of a circumscriptible n-simplex, and we prove a double inequality involving the circumradius and the edge-inradius of such simplices. With these results a part of a problem posed by the authors is solved.
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