In this paper we give generalization of Opial-type inequalities by using generalized fractional integral operator involving generalized Mittag–Leffler function. We deduce some results which already have been proved. Also we consider n -exponential convexity of some non-negative differences of inequalities involving Mittag-Leffler function and deduce their exponential convexity and log-convexity.

In this paper, we define the modular space Z σ (s, p) by using the Zweier operator and a modular. Then, we consider it equipped with the Luxemburg norm and also examine the uniform Opial property and property β. Finally, we show that this space has the fixed point property.

On the OrliczCesaro sequence spaces ( ces ) which are defined by using Orlicz function , we show that the space ces equipped with both Amemiya and Luxemburg norms possesses uniform Opial property and uniform Kadec-Klee property if satisfy the 52 -condition.