Superquadratic function is a generalization of convex functions. Results based on superquadratic functions are more refined than the results obtained using the notion of convexity. This work aims to provide a new class of superquadratic functions called superquadratic fuzzy-interval-valued function (superquadrtic $F_{I.V.F}$) and demonstrate its properties using fuzzy order relations. In the space of fuzzy intervals, this relation is also termed as the Kulisch-Miranker order relation defined on such a space level-wise. By leveraging the definition and features of superquadrtic $F_{I.V.F}$, we come up with improved integral inequalities such as Hermite-Hadamard (H.H) and Jensen type for superquadrtic $F_{I.V.F}$. Furthermore, we offer fractional representation of inequalities of H.H's types for superquadrtic $F_{I.V.F}$ with respect to fuzzy interval Riemann-Liouville fractional integral operators. These findings are further validated through specific numerical examples and graphical illustrations, which demonstrate the practical relevance and applicability of the results. We have no doubt that these results will open new avenues for researchers to further explore the notion of superuadraticity.

In this paper, we introduce a new hybrid relaxed iterative algorithm with two half-spaces to solve the fixed-point problem and split-feasibility problem involving demicontractive mappings. The strong convergence of the iterative sequence produced by our algorithm is proved under certain weak conditions. We give several numerical experiments to demonstrate the efficiency of the proposed iterative method in comparison with previous algorithms.

We introduce an alternated inertial subgradient extragradient algorithm of non-Lipschitz and pseudo-monotone operators to solve variational inequality and fixed point problems. We also demonstrated that, under certain conditions, the sequence produced by our algorithm exhibits weak convergence. Moreover, some numerical experiments have been proposed to compare our algorithm with previous algorithms in order to demonstrate the effectiveness of our algorithm.