Abstract. We consider unbounded spin systems on the one dimensional Lattice with interactions that go beyond the usual strict convexity and without uniform bound on the second derivative. We assume that the one dimensional without interactions (boundary-free) measure satisfies the Log-sobolev inequality and we determine conditions under which the Log-Sobolev Inequality can be extended to the in...

* Correspondence: [email protected] Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan Full list of author information is available at the end of the article Abstract We consider functionals due to the difference in Petrović and related inequalities and prove the log-convexity and exponential convexity of these functionals by using different families of functions...

In this paper we extend complex uniform convexity estimates for $\mathbb{C}$ to $\mathbb{R}^n$ and determine best constants. Furthermore, provide the link log-Sobolev inequalities hypercontractivity ultraspherical measures.

Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain including extended type Gauss hypergeometric function confluent function, respectively, virtue Hölder integral inequality Chebyshev’s inequality. We also studied monotonicity, log-concavity, log-convexity functions, which are deri...

We develop a parallel theory to that concerning the concept of integral mean value of a function, by replacing the additive framework with a multiplicative one. Particularly, we prove results which are multiplicative analogues of the Jensen and Hermite-Hadamard inequalities. 1. Introduction Many results in Real Analysis exploits the property of convexity of the subintervals I of R; (A) x; y 2 I...

In this paper, the author presents some double inequalities involving a ratio of v-Gamma and v-polygamma functions. The approach makes use log-convexity property function monotonicity function. Some results also give generalizations extensions previous results.