Some New Hermite-Hadamard Type Inequalities Via k-Fractional Integrals Concerning Differentiable Generalized Relative Semi-(r;m,p,q,h1,h2)-Preinvex Mappings

In this article, we first presented a new identity concerning differentiable mappings defined on m-invex set via k-fractional integrals. By using the notion of generalized relative semi-(r;m,p,q,h1,h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

Radius of Convexity of Sections of a Class of Close-to-Convex Functions of Order α

In this paper we study radius of convexity of sections of a class of univalent close-to-convex functions on 𝔻 = {z ∈ ℂ: |z| < 1}. For functions in this class, coefficient bounds, an integral representation and radius of convexity of nth sections have been obtained.

Remarks on *−(σ,Τ)− Lie Ideals of *−Prime Rings with Derivation

Let R be a ∗−prime ring with characteristic not 2, U a nonzero ∗− (σ,τ)−Lie ideal of R, d a nonzero derivation of R. Suppose σ, τ be two automorphisms of R such that σd = dσ, τd = dτ and ∗ commutes with σ, τ, d. In the present paper it is shown that if d(U) ⊆ Z or d2(U) ⊆ Z, then U ⊆ Z.

Opial and Pólya Type Inequalities Via Convexity

In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale 𝕋. We will derive the integral and discrete inequalities of Pólya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.

Some Common Coupled Fixed Point Theorems in Sb-Metric Spaces

In this paper, we prove some common coupled fixed point theorems for mapping satisfying a nonlinear contraction in Sb-metric space and some results are also given in the form of corollary. Also, some examples are given to verify the main results.

Connected Domination Polynomial of Graphs

Let G be a simple graph of order n. The connected domination polynomial of G is the polynomial $D_c \left( {G,x} \right) = \sum\nolimits_{i = \gamma _c \left( G \right)}^{\left| {V\left( G \right)} \right|} {d_c \left( {G,i} \right)x^i }$ , where dc(G,i) is the number of connected dominating sets of G of size i and γc(G) is the connected domination number of G. In this paper we study Dc(G,x) of any graph. We classify many families of graphs by studying their connected domination polynomial.

Some Properties of Rectifiable Spaces

In this paper, we give some properties of rectifiable spaces and their relationship with P-space, metrizable space. These results are used to generalize some results in [2], [9] and [12]. Moreover, we give the conditions for a rectifiable space to be second-countable.

Normal Families and Shared Functions

Let k ∈ ℕ, m ∈ℕ ∪{0}, and let a(z)(≢ 0) be a holomorphic function, all zeros of a(z) have multiplicities at most m. Let ℱ be a family of meromorphic functions in D. If for each f ∈ℱ, the zeros of f have multiplicities at least k + m + 1 and all poles of f are of multiplicity at least m + 1, and for f,g ∈ℱ, ff(k)−a(z) and gg(k)−a(z) share 0, then ℱ is normal in D. Some examples are given to show that the conditions are best, and the result removes the condition “m is an even integer” in the result due to Sun [Kragujevac Journal of Math 38(2), 173-282, 2014].

Approximation by Max-Product Operators

Here we study the approximation of functions by a great variety of Max-Product operators under differentiability. These are positive sublinear operators. Our study is based on our general results about positive sublinear operators. We produce Jackson type inequalities under initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. We improve known related results which do not use smoothness of functions..

On Regulated Functions

In this paper we investigate the space of regulated functions on a compact interval [0,1]. When equipped with the topology of uniform convergence this space is isometrically isomorphic to some space of continuous functions. We study some of its properties, including the characterization of the dual space, weak and strong compactness properties of sets. Finally, we investigate some compact and weakly compact operators on the space of regulated functions. The paper is complemented by an existence result for the Hammerstein-Stieltjes integral equation with regulated solutions.