In this paper, the authors introduce the generalization of Hermite-Hadamard inequality by using ( M φ , M ψ ) -convex functions and getting some other theorems with ( M φ , M ψ ) -convex functions. Some natural applications to special means of real numbers are also given.

Let 0 ≤ α < n , M α be the fractional maximal operator, M ♯ be the sharp maximal operator and b be the locally integrable function. Denote by [ b , M α ] and [ b , M ♯ ] be the commutators of the fractional maximal operator M α and the sharp maximal operator M ♯ . In this paper, we show some necessary and sufficient conditions for the boundedness of the commutators [ b , M α ] and [ b , M ♯ ] on slice spaces when the function b is the Lipschitz function, by which some new characterizations of the non-negative Lipschitz function are obtained.

Demi versions of different classes of operators have been recently investigated by many researchers. In this paper we study the demi version of quasi Levi and Levi operators. We investigate their properties. Moreover, their relations with other classes of operators are also discussed.

In this paper we introduce the notion of a DC-prime filter in BL-algebras and obtain some theorems in order to determine the relationships between this notion and some types of filters in a BL-algebra. By some examples, we show that each of these concepts is different from the other. Also, using the notion of DC-prime filters, a new class of BL-algebras are defined and studied.

A convex function f : [a,b] → ℝ satisfies the so-called Hermite-Hadamard inequality f (a + b 2 ) ≤ 1 b − a∫ abf(t)dt ≤f(a) + f(b) 2 . Motivated by the above estimates, in this paper we consider approximately monotone and convex functions, and give upper and lower bounds to the numerical integral mean, i.e., to 1 b−aIn(f), where In(f) denotes some of the most popular Newton-Cotes quadrature formulas.

In this paper, we introduce the notion of the generalized ternary ring homomorphism on non-Archimedean ternary Banach algebras. Using fixed point methods, we prove the superstability and generalized Hyers-Ulam stability of generalized ternary ring homomorphisms on non-Archimedean ternary Banach algebras associated with a Cauchy-Jensen type functional equation.

In this work, Weyl’s famous classification was made for singular impulsive Hahn–Sturm–Liouville equations.

In this paper, we prove significant results related to the Hermite-Hadamard inequality for convex functions in the framework of Riemann-Liouville fractional integrals with variable order. Two novel equalities are proved to have new fractional trapezoid and midpoint-type inequalities for the differentiable convex functions. This work provides a computational analysis of these inequalities, with numerical examples for convex functions. Additionally, it is demonstrated that the newly identified inequalities represent a generalisation of the comparable inequalities in the literature.

In this paper, concepts of (cofinitely) ( D 12 ∗ ) -modules which are a proper generalization of concept of ⊕ δ -supplemented modules are studied. We say that M is a ( D 12 ∗ ) -module if for every submodule A of M , there exists a direct summand B of M and an epimorphism f : B → M A such that ker ( f ) ≪ δ B . The module M is called cofinitely ( D 12 ∗ ) -module if for every cofinite submodule A of M , there exists a direct summand B of M and an epimorphism f : B → M A such that ker ( f ) ≪ δ B . In this paper, various properties of these modules are given. In addition, a new characterization of δ -semiperfect rings is given using cofinitely ( D 12 ∗ ) -modules.

Tolerance relations were investigated by several authors in various algebraic structures, see e.g. the monograph [1]. Recently G. Czédli [5] proved that two 2 -uniform tolerances on a lattice containing no infinite chain permute if and only if they are amicable. We extend this result to tolerances on posets. Since in posets we have no lattice operations, we modify the notion of amicability in such a way that in case of lattices it coincides with the original definition. With this new definition we can prove that two 2 -uniform tolerances on a poset containing no infinite chain permute if and only if they are amicable.