Mapping properties of integral operator involving some special functions

OMA-Vol. 1 (2017), Issue 1, pp. 34–43 | Open Access Full-Text PDF
Muhey U Din, Mohsan Raza, Saddaf Noreen
Abstract:In this article, we are mainly interested to find some sufficient conditions for integral operator involving normalized Struve and Dini function to be in the class \(N\left( \mu \right)\). Some corollaries involving special functions are also the part of our investigations.
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K-Banhatti and K-hyper Banhatti indices of dominating David Derived network

OMA-Vol. 1 (2017), Issue 1, pp. 13–24 | Open Access Full-Text PDF
Wei Gao, Batsha Muzaffar, Waqas Nazeer
Abstract: Let \(G\) be connected graph with vertex \(V(G)\) and edge set \(E(G)\). The first and second \(K\)-Banhatti indices of \(G\) are defined as \(B_{1}(G)=\sum\limits_{ue}[d_{G}(u)+d_{G}(e)]\) and \(B_{2}(G)=\sum\limits_{ue}[d_{G}(u)d_{G}(e)]\) ,where \(ue\) means that the vertex \(u\) and edge \(e\) are incident in \(G\). The first and second \(K\)-hyper Banhatti indices of \(G\) are defined as \(HB_{1}(G)=\sum\limits_{ue}[d_{G}(u)+d_{G}(e)]^{2}\) and \(HB_{2}(G)=\sum\limits_{ue}[d_{G}(u)d_{G}(e)]^{2}\). In this paper, we compute the first and second \(K\)-Banhatti and \(K\)-hyper Banhatti indices of Dominating David Derived networks.
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An implicit viscosity technique of nonexpansive mapping in CAT(0) spaces

OMA-Vol. 1 (2017), Issue 1, pp. 1–12 | Open Access Full-Text PDF
Iftikhar Ahmad, Maqbool Ahmad
Abstract: In this paper, we present a new viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorems of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature.
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Computing Sanskruti Index of Titania Nanotubes

OMS-Vol. 1 (2017), Issue 1, pp. 126–131 | Open Access Full-Text PDF
Muhammad Shoaib Sardar, Xiang-Feng Pan, Wei Gao, Mohammad Reza Farahani
Abstract:Let \(G=(V;E)\) be a simple connected graph. The Sanskruti index was introduced by Hosamani and defined as \(S(G)=\sum_{uv \in E(G)}(\frac{S_uS_v}{S_u+S_v-2})^3\) where \(S_u\) is the summation of degrees of all neighbors of vertex \(u\) in \(G\). In this paper, we give explicit formulas for the Sanskruti index of an infinite class of Titania nanotubes \(TiO_2[m, n]\).
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Ostrowski Type Fractional Integral Inequalities for S -Godunova-Levin Functions via Katugampola Fractional Integrals

OMS-Vol. 1 (2017), Issue 1, pp. 97–110 | Open Access Full-Text PDF
Ghulam Farid, Udita N. Katugampola, Muhammad Usman
Abstract:In this paper, we give some fractional integral inequalities of Ostrowski type for s-Godunova-Levin functions via Katugampola fractional integrals. We also deduce some known Ostrowski type fractional integral inequalities for Riemann-Liouville fractional integrals.
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Analytical Solution for the Flow of a Generalized Oldroyd-B Fluid in a Circular Cylinder

OMS-Vol. 1 (2017), Issue 1, pp. 85–96 | Open Access Full-Text PDF
Haitao Qi, Nida Fatima, Hassan Waqas, Junaid Saeed
Abstract:The tangential stress and velocity field corresponding to the flow of a generalized Oldroyd-B fluid in an infinite circular cylinder will be determined by mean of Laplace and finite Hankel transform. The motion is produced by the cylinder, that after \(t=0^{+}\), begins to rotate about its axis, under the action of oscillating shear stress \(\Omega R \sin(\omega t)\) given on boundary. The solutions are based on an important remark regarding the governing equation for the non- trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The obtained solution will be presented under series form in term of generalized G-function. The similar solutions for the ordinary Oldroyd-B fluid, Maxwell, ordinary Maxwell and Newtonian fluids performing the same motion will be obtained as special cases of our general solutions.
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Kauffman Bracket of 2- and 3-Strand Braid Links

OMS-Vol. 1 (2017), Issue 1, pp. 72–84 | Open Access Full-Text PDF
Abdul Rauf Nizami
Abstract:In this paper we give explicit formulas of the Kauffman bracket of the 2-strand braid link \(\widehat{x_{1}^{n}}\) and the 3-strand braid link \(\widehat{x_{1}^{b}x_{2}^{m}}\). We also show that the Kauffman bracket of the 3-strand braid link \(\widehat{x_{1}^{b}x_{2}^{m}}\) is actually the product of the Kauffman brackets of the 2-strand braid links \(\widehat{x_{1}^{b}}\) and \(\widehat{x_{1}^{m}}\).
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Computing topological indices of Hex Board and its line graph

OMS-Vol. 1 (2017), Issue 1, pp. 62–71 | Open Access Full-Text PDF
Hafiz Mutee ur Rehman, Riffat Sardar, Ali Raza
Abstract:A topological index is a real number related to a molecular graph, which is a graph invariant. Uptill now there are several topological indices are defined. Some of them are distance based while the others are degree based, all have found numerous applications in pharmacy, theoretical chemistry and especially in QSPR/QSAR research. In this paper, we compute some degree based topological indices i.e some versions of Zagreb indices, Randic index, General sum connectivity index and GA index of Hex board and of its line graph.
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