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In this paper, the definition of the harmonically c r -h-convex function is given, and its important properties are discussed. Jensen type inequality, Hermite–Hadamard type inequalities and Fejér type inequalities for harmonically c r -h-convex functions are also established. In addition, some numerical examples are given to verify the accuracy of the results. [ABSTRACT FROM AUTHOR]

This paper is devoted to derive optimality conditions and duality theorems for interval-valued optimization problems based on gH-symmetrically derivative. Further, the concepts of symmetric pseudo-convexity and symmetric quasi-convexity for interval-valued functions are proposed to extend above optimization conditions. Examples are also presented to illustrate corresponding results. [ABSTRACT FROM AUTHOR]

This paper is devoted to establishing some Hermite–Hadamard-type inequalities for interval-valued functions using the coordinated h-convexity, which is more general than classical convex functions. We also discuss the relationship between coordinated h-convexity and h-convexity. Furthermore, we introduce the concepts of minimum expansion and maximum contraction of interval sequences. Based on these two new concepts, we establish some new Hermite–Hadamard-type inequalities, which generalize some known results in the literature. Additionally, some examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this article, we study a class of Choquard–Kirchhoff type equations driven by the variable s (x , ·) -order fractional p 1 (x , ·) and p 2 (x , ·) -Laplacian. Assuming some reasonable conditions and with the help of variational methods, we reach a positive energy solution and a negative energy solution in an appropriate space of functions. The main difficulties and innovations are the Choquard nonlinearities and Kirchhoff functions with the presence of double Laplace operators involving two variable parameters. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of Schrödinger–Poisson systems with critical growth. By the principle of concentration compactness and variational methods, we prove that the system has radially symmetric solutions, which improve the related results on this topic. [ABSTRACT FROM AUTHOR]

In this paper, firstly we prove the relationship between interval h-convex functions and interval harmonically h-convex functions. Secondly, several new Hermite–Hadamard type inequalities for interval h-convex functions via interval Riemann–Liouville type fractional integrals are established. Finally, we obtain some new fractional Hadamard–Hermite type inequalities for interval harmonically h-convex functions by using the above relationship. Also we discuss the importance of our results and some special cases. Our results extend and improve some previously known results. [ABSTRACT FROM AUTHOR]

We introduce the concept of interval (h 1 , h 2) -convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples. [ABSTRACT FROM AUTHOR]