Waqas Nazeer

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the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we establish a new third order iterative method for solving nonlinear equations. The efficiency index of the method is 1.442 2 which is the equal to the Halley's and(More)
In this paper, we present a modified two-step fixed point iterative method for solving nonlinear functional equations and analyzed. The modified two-step fixed point iterative method has convergence of order two. The modified two-step fixed point iterative method converges faster than the fixed point method. The comparison table demonstrates the faster(More)
In this paper, we present a new fixed point iterative method for solving nonlinear functional equations and analyzed. The new fixed point iterative method has convergence of order two. The new fixed point iterative method converges faster than the fixed point method. The comparison table demonstrates the faster convergence of new fixed point method. 1(More)
In this paper, we present a new modified two-step Jungck iterative method (NMJIM) for solving nonlinear functional equations and analyzed. The new modified two-step Jungck iterative method has convergence of order five and efficiency index 2.2361 which is larger than all Jungck type iterative methods and the methods discussed in Table 1. The new modified(More)
A radio k-labeling c of a graph G is a mapping c : V (G) → Z + ∪{0} such that d(u, v)+|c(u)−c(v)| ≥ k+1 for every two distinct vertices u and v of G, where d(u, v) is the distance between any two vertices u and v of G. The span of a radio k-labeling c is denoted by sp(c) and defined as max{|c(u) − c(v)| : u, v ∈ V (G)}. The radio labeling is a radio(More)
Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate(More)
In this paper, we suggest and analyze two new iterative methods for solving nonlinear scalar equations namely: the modified generalized Newton Raphson's method and generalized Newton Raphson's method free from second derivative are having convergence of order six and five respectively. We also give several examples to illustrate the efficiency of these(More)
In this note, we give fixed point results in fractal generation (Julia sets and Mandelbrot sets) by using Noor iteration scheme with s-convexity. Researchers have already presented fixed point results in Mann and Ishikawa orbits that are examples of one-step and two-step feedback processes respectively. In this paper we present fixed point results in Noor(More)
Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical(More)
Let G be a connected graph with diameter diam () G and (,) d x y denotes the shortest distance between any two distinct vertices , xy in G. Radio labeling (multi-level distance labeling or distance labeling) of G is a one-to-one mapping : () {0} f V G Z   satisfying (,) | () () | () 1 d x y f x f y diam G     for all , () x y V G . The span of a(More)