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We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice based on equality of the topologies induced by uninorms. [ABSTRACT FROM AUTHOR]

In this paper, the normalizers of Γ0k(n), for k = 2 or 3, in the groups Γk of modular group Γ are given by using the concept of Γk axes of the set of left cosets of Γ0k(n), on which Γk acts transitively, in Γk. [ABSTRACT FROM AUTHOR]

In this paper, we prove three new Katugampola fractional Hermite-Hadamard type inequalities for harmonically convex functions by using the left and the right fractional integrals independently. One of our Katugampola fractional Hermite-Hadamard type inequalities is better than given in [17]. Also, we give two new Katugampola fractional identities for differentiable functions. By using these identities, we obtain some new trapezoidal type inequalities for harmonically convex functions. Our results generalize many results from earlier papers. [ABSTRACT FROM AUTHOR]

In this paper, we gave adjustments for some results in the paper [1], and proved three new Katugampola fractional Hermite-Hadamard type inequalities for convex functions by using the left and the right fractional integrals independently. One of our Katugampola fractional Hermite-Hadamard type inequalities is better than given by Chen and Katugampola. Also, we gave two new Katugampola fractional identities for differentiable functions. By using these identities, we obtained some new trapezoidal type inequalities for convex functions. Our results generalize earlier results. [ABSTRACT FROM AUTHOR]

In this paper, we prove three new conformable fractional Hermite-Hadamard type inequalities for harmonically convex functions by using the left and the right fractional integrals independently. Also, we give two new conformable fractional identities for differentiable functions. By using these identities, we obtained some new trapezoidal type inequalities for harmonically convex functions. Our results generalizes the results given by İşcan in [5] and Sanli et al. in [18]. [ABSTRACT FROM AUTHOR]

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In this paper, we define an invariant equivalence relation by using the group Ɣ (2). Then we investigate some combinatorial properties of subgraphs of Ɣ2. [ABSTRACT FROM AUTHOR]

In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice L. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice L, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm. [ABSTRACT FROM AUTHOR]

Let q ≥ 2 integer. Then the projective special linear groups PSL(2, q) ≅ SL(2, q)/Z, where Z is the central subgroup of SL(2, q) consisting of the scalar matrices with determinant equal to 1. PSL(2, q) is the most frequently studied subgroup of the modular group. The elements of this group correspond to matrices of SL(2, q). In this study, for q = 5 we find all triangles circuits, loops and paths in blocks. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new estimates on generalization of Hermite-Hadamard, Ostorowski and Simpson type inequalities for Lipschitzian functions via Riemann-Liouville fractional integrals. Also, we give some applications to special means of two positive real numbers. [ABSTRACT FROM AUTHOR]