This paper is devoted to novel diamond alpha Hardy–Copson type dynamic inequalities, which are (Formula presented.) complements of the classical ones obtained for (Formula presented.) and their applications to difference ...

Calculus for dynamic equations on time scales, which offers a unification of discrete and continuous systems, is a recently developed theory. Our aim is to investigate Constantin's inequality on time scales that is an ...

In this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that ...

We give a discrete Gruss type inequality on fractional calculus

We prove some new inequalities of Mitrinović–Pečarić inequalities for convex functions on an arbitrary time scale using delta integrals. These inequalities extend and improve some known dynamic inequalities in the literature. ...

We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this ...

Properties of the discrete fractional calculus in the sense of a backward difference are introduced and developed. Here, we prove a more general version of the Gruss type inequality for the nabla fractional case. An example ...

In this manuscript, we extend, generalize and enrich some recent coupled fixed point theorems in the framework of partially ordered G-metric spaces in a way that is essentially more natural.

Some new criteria for the oscillation of even order linear dynamic equations on time-scales of the form xΔn(t) + q(t)x(t) = 0 are established.

We extend classical nabla and delta Hardy-Copson type inequalities from zeta > 1 to 0 < zeta < 1 and also use these novel inequalities to find necessary and sufficient condition for the nonoscillation of the related half ...