Faisal Ali

Faisal Ali
Bahauddin Zakariya University | BZU · Centre for Advanced Studies in Pure and Applied Mathematics

PhD

About

45
Publications
10,229
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196
Citations
Citations since 2016
28 Research Items
171 Citations
201620172018201920202021202201020304050
201620172018201920202021202201020304050
201620172018201920202021202201020304050
201620172018201920202021202201020304050
Additional affiliations
January 1995 - February 2017
Bahauddin Zakariya University
Position
  • Professor (Associate)

Publications

Publications (45)
Article
Full-text available
A bond-additive connectivity index, named as the Mostar index, is used to measure the amount of peripheral edges of a simple connected graph, where a peripheral edge in a graph is an edge whose one end vertex has more number of vertices closer as compared to the other end vertex. In this study, we count the contribution of peripheral edges in commu...
Article
In the present paper, we develop an efficient second derivative free two-step optimal fourth-order iterative method for nonlinear equations. We explore the convergence criteria of the proposed method and also exhibit its validity and efficiency by considering some test problems. We present both numerical as well as graphical comparisons. Further, t...
Article
Full-text available
We use the homotopy perturbation method (HPM) to construct a new iterative system for solving non-linear equations in this article. The criteria for convergence in the scheme developed are also imposed. To show the validity and reliability of our process, we compare our regime with other current procedures by looking at various test problems.
Article
Full-text available
Several bioactivities of chemical compounds in a molecular graph can be expected by using many topological descriptors. A topological descriptor is a numeric quantity which quantify the topology of a graph. By defining the metric on a graph related with a vector space, we consider this graph in the context of few topological descriptors, and quanti...
Article
Full-text available
Various iterative methods have been introduced by involving Taylor’s series on the auxiliary function gx to solve the nonlinear equation fx=0. In this paper, we introduce the expansion of gx with the inclusion of weights wi such that ∑i=1pwi=1 and knots τi∈0,1 in order to develop a new family of iterative methods. The methods proposed in the presen...
Article
Most of the problems in mathematical and engineering sciences can be studied in the context of nonlinear equations. In this paper, we develop a new family of iterative methods for the approximation of the zeros of mathematical models whose governing equations are nonlinear in nature. The proposed methods are based on decomposition technique due to...
Article
Full-text available
Background The valency of an atom in a molecular structure is the number of its neighboring atoms. A large number of valency based molecular invariants have been conceived, which correlate certain physio-chemical properties like boiling point, stability, strain energy and many more of chemical compounds. Objective Our aim is to study the valency b...
Article
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Several properties of chemical compounds in a molecular structure can be determined with the aid of mathematical languages provided by various types of topological indices. In this paper, we consider eight den-drimer structures in the context of valency based topolog-ical indices. We define four Banhatti polynomials for general (molecular) graphs,...
Article
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A topological index is actually designed by transforming a chemical structure into a number. Topo-logical index is a graph invariant which characterizes the topology of the graph and remains invariant under graph automorphism. Eccentricity based topological indices are of great importance and play a vital role in chemical graph theory. In this arti...
Article
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The metric is a non-negative assignment to the pairs of nodes in a connected network N, which assigns the number of links lying in a smallest path between the nodes in the pairs. A pair (a; b) of nodes in N is said to be uniquely identified by a node c of N if the metric assigned to the pair (a; c) is different from the metric assigned to the pair...
Article
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A vertex v of a graph G uniquely determines(resolves) a pair (v1,v2) of vertices of G if the distance between v and v1 is different from the distance between v and v2. The metric index is a distance based topological index of a graph G, which is the least number of vertices in G chosen in such a way that each vertex of G can be determined uniquely...
Article
The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Alghamdi et al. [The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), Article ID 96, 9 pages] associated with ϕ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach sp...
Article
Full-text available
A topological index is a numerical value associated with the chemical constitution for the correlation of chemical structures with various physical properties, chemical reactivity or biological activity. A large number of graph-distance-based topological indices in various families of graphs and networks have been computed. In this paper, we consid...
Article
We study the convergence of implicit midpoint type Picard sequence for strongly accretive and strongly pseudocontractive mappings. We have also improved the results of some authors.
Article
In this paper, using the system of coupled equations involving an auxiliary function, we introduce some new efficient higher order iterative methods based on modified homotopy perturbation method. We study the convergence analysis and also present various numerical examples to demonstrate the validity and efficiency of our methods.
Article
Full-text available
In this paper, using the system of coupled equations involving an auxiliary function, we introduce some new efficient higher order iterative methods based on modified homotopy perturbation method. We study the convergence analysis and also present various numerical examples to demonstrate the validity and efficiency of our methods.
Article
In this paper, we introduce two new iteration schemes, namely modified Mann and modified Ishikawa to approximate the fixed points of quasi contractive operators on a normed space. Various test problems are presented to reveal the validity and high efficiency of these iterative schemes.
Article
Full-text available
This paper is concerned with the (p,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}-analog of Bernstein operators. It is proved that, when the fun...
Article
We prove the existence of the common fixed point for three asymptotically nonexpensive mappings defined on a A-uniformly convex metric space. A three-step iterative scheme is constructed which converges to the common fixed point. We also generalize the results of several authors.
Article
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Let Γ be a non-abelian group and Ω ⊆ Γ. We define the commuting graph G = 풞(Γ, Ω) with vertex set Ω and two distinct elements of Ω are joined by an edge when they commute in Γ. In this article, among some properties of commuting graphs, we investigate distant properties as well as detour distant properties of commuting graph on D2n. We also study t...
Article
In this paper, we establish new iterative methods for the solution of scalar equations by using the decomposition technique mainly due to Daftardar-Gejji and Jafari [V. Daftardar-Gejji, H. Jafari, J. Math. Anal. Appl., 316 (2006), 753–763].
Article
Full-text available
In this paper, we establish new iterative methods for the solution of scalar equations by using the decomposition technique due to Noor and Noor [Some iterative schemes for nonlinear equations, Appl. Math. Comput. 183 (2006), 774-779].
Article
In this paper, we establish new iterative methods for the solution of scalar equations by using the decomposition technique given in [17] (M. A. Noor and K. I. Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput., 183 (2006), 774-779).
Article
In this paper, we develop a new iterative method to approximate the root of a scalar nonlinear equation. Our method is the modification of standard Newton's method with the same number of function and derivative evaluations at each iteration. We present a comparison of the new method with some other well known methods.
Article
Full-text available
In this paper we study the geometry of relative superior Mandelbrot sets through S-iteration scheme. Our results are quit significant from other Mandelbrot sets existing in the literature. Besides this, we also observe that S-iteration scheme converges faster than Ishikawa iteration scheme. We believe that the results of this paper can be inspired...
Article
We prove the existence of a fixed point for asymtotically nonexpensive mappings defined on a unifromly convex metric space. An modified two-stepIshikawa type iterative scheme is constructed which converges to the fixed point.
Article
In this paper, a new iterative method for solving nonlinear equations is developed by using modified homotopy perturbation method. The convergence analysis of the proposed method is also given. The validity and efficiency of our method is illustrated by applying this new method along with some other existing methods on various test problems.
Conference Paper
Full-text available
Polynomiography is the art and science of visualization in approximation of zeros of complex polynomial. The purpose of this paper is to present some modifications of visualization process using S-iteration scheme. A new iteration method is used instead of Newton method to create polynomiographs of complex polynomials. By using new iteration method...
Conference Paper
Full-text available
In this paper, we present the generalization of Julia sets and Mandelbrot sets for complex-valued polynomials such as quadratic, cubic and n-th degree polynomials using Jungck three-step orbit. The generation of few Julia sets and Mandelbrot sets in Jungck three-step orbit are shown in form of examples.
Article
Polynomiography is the art and science of visualization in approximation of zeros of complex polynomial. The purpose of this paper is to present some modifications of visualization process using S-iteration scheme. A new itera- tion method is used instead of Newton method to create polynomiographs of complex polynomials. By using new iteration meth...
Article
Full-text available
In this paper, we present the generalization of Julia sets and Mandelbrot sets for complex-valued polynomials such as quadratic, cubic and n-th degree polynomials using Jungck three-step orbit. The generation of few Julia sets and Mandelbrot sets in Jungck three-step orbit are shown in form of examples.
Article
The aim of this paper is to introduce the relative superior Julia sets by using S-iteration scheme. Relative superior Julia sets are further generalization of Julia sets for complex-valued polynomials using S-iteration orbit. Julia sets live in complex plane and are non empty. Graphical images of Julia sets have been visualized and certain patterns...
Article
In this paper, we establish the strong convergence for the Ishikawa iterative scheme associated with Lipschitz pseudocontractive mappings in real Banach spaces.
Article
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Let.. be a nonempty closed convex subset of a real Banach space E, let K -> K be nonexpansive, and let T : K -> K be Lipschitz strongly pseudocontractive mappings such that p epsilon F(S) boolean AND F(T) = {x epsilon K : Sx = Tx + x } and ||x - Sy|| <= ||Sx -Sy|| and ||x -Ty|| for all x, y epsilon K. Let {beta(n)} be a sequence in [0, 1] satisfyin...
Article
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Following the approach of [R. K. Pandey et al., Appl. Math. Comput. 218, No. 14, 7629–7637 (2012; Zbl 1246.65115)], in this paper, an approach using tau method based on Legendre operational matrix of differentiation has been introduced for solving general form of second order linear and nonlinear ordinay differential equations. With the implementat...
Article
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We prove continuity of the Riesz potential operator in optimal couples of rearrangement invariant function spaces defined in Rn with the Lebesgue measure. MSC: 46E30, 46E35.
Article
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In this paper, we establish strong convergence for the Agarwal et al. iterative scheme associated with Lipschitzian hemicontractive mappings in Hilbert spaces. MSC: 47H10, 47J25.
Article
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By taking a counterexample, we prove that the multistep iteration process is faster than the Mann and Ishikawa iteration processes for Zamfirescu operators.
Article
Let R be a 2-torsion free non-commutative ring with centre Z(R)≠{0}. Let F be a nonzero central generalized derivation, with associated central derivation d such that d(Z(R))={0}, of R. If for some nonzero c∈Z(R), R is cF-prime as well as cd-prime, then Z(R)F is a prime Lie ring.
Article
We investigate some properties of generalized (α,β)-derivations on semiprime rings. Among some other results, we show that if g is a generalized (α,β)-derivation, with associated (α,β)-derivation δ, on a semiprime ring R such that [g(x),α(x)]=0 for all x∈R, then δ(x)[y,z]=0 for all x,y,z∈R and δ is central. We also show that if α,ν,τ are endomorphi...
Article
We investigate some properties of generalized (α, β)-derivations on semiprime rings. Among some other results, we show that if g is a generalized (α, β)-derivation, with associated (α,β)-derivation δ, on a semiprime ring R such that [g(x), α(x)] = 0 for all x ∈ R, then δ(x)[y, z] = 0 for all x, y, z ∈ R and δ is central. We also show that if α, ν,...
Article
Full-text available
We characterize dependent elements of a commuting derivation d on a semiprime ring R and investigate a decomposition of R using dependent elements of d. We show that there exist ideals U and V of R such that U⊕V is an essential ideal of R, U∩V={0}, d=0 on U, d(V)⊆V, and d acts freely on V.

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