Open Journal of Mathematical Sciences (OMS)

In this paper, we establish viscosity rule for common fixed points of two 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 work extend and improve some recent announced in the literature.

In this work, we developed homotopy perturbation double Sumudu transform method (HPDSTM) which is obtained by combining homotopy perturbation method, double Sumudu transform and He’s polynomials. The method is applied to find the solution of linear fractional one and two dimensional dispersive KdV and nonlinear fractional KdV equations to illustrate the reliability of the method. It is observed that the solutions obtained by the method converge rapidly to the exact solutions. This method is very powerful, and professional techniques for solving different kinds of linear and nonlinear fractional order differential equations.

In this article, we compute closed forms of M-polynomial for three general classes of convex polytopes. From the M-polynomial, we derive degree-based topological indices such as first and second Zagreb indices, modified second Zagreb index, Symmetric division index, etc.

Let \(G\) be a simple connected molecular graph with vertex set \(V(G)\) and edge set \(E(G)\). One important modification of classical Zagreb index, called hyper Zagreb index \(HM(G)\) is defined as the sum of squares of the degree sum of the adjacent vertices, that is, sum of the terms \({[{{d}_{G}}(u)+{{d}_{G}}(v)]^2}\) over all the edges of \(G\), where \(d_G(v)\) denote the degree of the vertex \(u\) of \(G\). In this paper, the hyper Zagreb index of certain bridge and chain graphs are computed and hence using the derived results we compute the hyper Zagreb index of several classes of chemical graphs and nanostructures.

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 \(TiO_2[m, n]\).

In this paper, we introduce, for the first time, the viscosity rules for common fixed points of two nonexpansive mappings in Hilbert spaces. The strong convergence of this technique is proved under certain assumptions imposed on the sequence of parameters.

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.

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.

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 \(\widehat{x_{1}^{m}}\).

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.