General solution of casson fluid past a vertical plate subject to the time dependent velocity with constant wall temperature

OMA-Vol. 2 (2018), Issue 1, pp. 47–65 | Open Access Full-Text PDF
Allia Naseem
Abstract:Unsteady free convection flow of Casson fluid over an unbounded upright plate subject to time dependent velocity \(U_{o}f(t)\) with constant wall temperature has been carried out. By introducing dimensionless variables, the general solutions are obtained by Laplace transform method. The solution corresponding to Newtonian fluid for \(\gamma \rightarrow \infty\) is obtained as a limiting case. Exact solutions corresponding to (i) \(f(t)=f H(t)\), (ii) \(f(t)=f t^{a}\), \(a > 0 \) (iii) \( f(t)=f H(t)cos(\omega t)\) are also discussed as special cases of our general solutions. Expressions for shear stress in terms of skin friction and the rate of heat transfer in the form of Nusselt number are also presented. Velocity and temperature profiles for different parameters are discussed graphically.
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New type integral inequalities for three times differentiable preinvex and prequasiinvex functions

OMA-Vol. 2 (2018), Issue 1, pp. 33–46 | Open Access Full-Text PDF
Huriye Kadakal, Mahir Kadakal, İmdat İşcan
Abstract: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.
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Non-convex hybrid method corresponding to Karakaya iterative process

OMA-Vol. 2 (2018), Issue 1, pp. 08–18 | Open Access Full-Text PDF
Samina Kausar, Muhammad Asif, Mubeen Munir
Abstract: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.
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A new third-order iteration method for solving nonlinear equations

OMA-Vol. 2 (2018), Issue 1, pp. 01–07 | Open Access Full-Text PDF
Muhammad Saqib, Zain Majeed, Muhammad Quraish, Waqas Nazeer
Abstract: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).
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Secure Domination in Lict Graphs

OMS-Vol. 2 (2018), Issue 1, pp. 134–145 | Open Access Full-Text PDF
Girish V. Rajasekharaiah, Usha P. Murthy
Abstract: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.
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On Moduli and Constants of quasi-Banach Spaces

OMS-Vol. 2 (2018), Issue 1, pp. 122–133 | Open Access Full-Text PDF
Hussain Minhaj Uddin Ahmad Qadri, Qaisar Mehmood
Abstract: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.
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Super \((a,d)\)-\(C_4\)-antimagicness of book graphs

OMS-Vol. 2 (2018), Issue 1, pp. 115–121 | Open Access Full-Text PDF
Muhammad Awais Umar, Malik Anjum Javed, Mujtaba Hussain, Basharat Rehman Ali
Abstract: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 \(n\geq2\).
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