In this paper, a new identity for functions defined on an open invex subset of set of real numbers is established, and by using the this identity and the Hölder and Power mean integral inequalities we present new type integral inequalities for functions whose powers of third derivatives in absolute value are preinvex and prequasiinvex functions.

In this paper, we gave the new general identity for differentiable function. As a result of this identity some new and general fractional integral inequalities for differentiable harmonically convex functions are obtained.

In this article we present non-convex hybrid iteration algorithm corollaryresponding to Karakaya iterative scheme [1] as done by Guan et al. in [2] corollaryresponding to Mann iterative scheme [3]. We also prove some strong convergence results about common fixed points for a uniformly closed asymptotic family of countable quasi-Lipschitz mappings in Hilbert spaces.

In this paper, we establish a two step third-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.442 which is greater than Newton-Raphson method. It is important to note that our method is performing very well in comparison to fixed point method and the method discussed by Kang et al. (Abstract and applied analysis; volume 2013, Article ID 487060).

In this paper we have presented a new method to compute the determinant of a \(5\times5\) matrix.

In this paper, some inequalities related to Čebyšev’s functional are proved.

For any graph \(G=(V,E)\), lict graph \(\eta(G)\) of a graph \(G\) is the graph whose vertex set is the union of the set of edges and the set of cut-vertices of \(G\) in which two vertices are adjacent if and only if the corresponding edges are adjacent or the corresponding members of \(G\) are incident. A secure lict dominating set of a graph \(\eta(G)\) , is a dominating set \(F \subseteq V(\eta(G))\) with the property that for each \(v_{1} \in (V(\eta(G))-F)\), there exists \(v_{2} \in F\) adjacent to \(v_{1}\) such that \((F-\lbrace v_{2}\rbrace) \cup \lbrace v_{1} \rbrace\) is a dominating set of \(\eta(G)\). The secure lict dominating number \(\gamma_{se}(\eta(G))\) of \(G\) is a minimum cardinality of a secure lict dominating set of \(G\). In this paper many bounds on \(\gamma_{se}(\eta(G))\) are obtained and its exact values for some standard graphs are found in terms of parameters of \(G\). Also its relationship with other domination parameters is investigated.

In this article we discuss moduli and constants of quasi-Banach space and give some important properties of these moduli and constants. Moreover, we establish relationships of these moduli and constants with each other.

Let \(G=(V,E)\) be a~finite simple graph with \(|V(G)|\) vertices and \(|E(G)|\) edges. An edge-covering of \(G\) is a family of subgraphs \(H_1, H_2, \dots, H_t\) such that each edge of \(E(G)\) belongs to at least one of the subgraphs \(H_i\), \(i=1, 2, \dots, t\). If every subgraph \(H_i\) is isomorphic to a given graph \(H\), then the graph \(G\) admits an \(H\)-covering. A graph \(G\) admitting \(H\) covering is called an \((a,d)\)-\(H\)-antimagic if there is a bijection \(f:V\cup E \to \{1,2,\dots, |V(G)|+|E(G)| \}\) such that for each subgraph \(H’\) of \(G \) isomorphic to \(H\), the sum of labels of all the edges and vertices belonged to \(H’\) constitutes an arithmetic progression with the initial term \(a\) and the common difference \(d\). For \(f(V)= \{ 1,2,3,\dots,|V(G)|\}\), the graph \(G\) is said to be super \((a,d)\)-\(H\)-antimagic and for \(d=0\) it is called \(H\)-supermagic. In this paper, we investigate the existence of super \((a,d)\)-\(C_4\)-antimagic labeling of book graphs, for difference \(d=0,1\) and \(n\geq2\).

In this article, the authors obtain the boundedness of the fractional Marcinkiewicz integral with variable kernel on Morrey-Herz spaces with variable exponents \(\alpha\) and \(p\). The corresponding boundedness for commutators generalized by the Lipschitz function is also considered.