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Integral Inequalities for Some New Classes of Convex Functions
Muhammad Aslam Noor,
Khalida Inayat Noor,
Muhammad Uzair Awan
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
1-5
Received:
19 March 2015
Accepted:
21 March 2015
Published:
9 June 2015
Abstract: In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.
Abstract: In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper conti...
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General Solution for Free Convection of Viscous Fluid Near an Infinite Isothermal Vertical Plate that Applies a Shear Stress to the Rotating Fluid
M. A. Imran,
Shakila Sarwar,
D. Vieru,
M. Nazar
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
6-13
Received:
19 May 2015
Accepted:
20 May 2015
Published:
9 June 2015
Abstract: An analysis is carried out to the unsteady free convection flow of a rotating, incompressible viscous fluid near an infinite vertical plate that applies a time-dependent shear stress f(t) to the fluid. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. At the final stage, the effects of pertinent parameters on the fluid motion are numerically and graphically illustrated. A comparison between the numerical values of the velocity components given by the analytical solution and, by the Stehfest's algorithm for the inverse Laplace transform is presented.
Abstract: An analysis is carried out to the unsteady free convection flow of a rotating, incompressible viscous fluid near an infinite vertical plate that applies a time-dependent shear stress f(t) to the fluid. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform...
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Odd Graceful Labeling of Acyclic Graphs
Ayesha Riasat,
Sana Javed
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
14-18
Received:
28 May 2015
Accepted:
30 May 2015
Published:
10 June 2015
Abstract: Let G = (V, E) be a finite, simple and undirected graph. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) {0, 1, 2, . . . , 2q 1} such that, when each edge xy is assigned the label |f (x) f (y)| , the resulting edge labels are {1, 3, 5, . . . , 2q 1} and f is called an odd graceful labeling of G. Motivated by the work of Z. Gao [6] in which he studied the odd graceful labeling of union of any number of paths and union of any number of stars, we have determined odd graceful labeling for some other union of graphs. In this paper we formulate odd-graceful labeling for disjoint unions of graphs consisting of generalized combs, stars, bistars and paths.
Abstract: Let G = (V, E) be a finite, simple and undirected graph. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) {0, 1, 2, . . . , 2q 1} such that, when each edge xy is assigned the label |f (x) f (y)| , the resulting edge labels are {1, 3, 5, . . . , 2q 1} and f is called an odd graceful labeling of G. Motivated b...
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Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
19-24
Received:
31 May 2015
Accepted:
1 June 2015
Published:
15 June 2015
Abstract: In this paper, we study the existence of positive solutions to a system of nonlinear differential equations subject to two-point coupled boundary conditions. Further, the nonlinearities are allowed to be singular with respect to first order derivatives. An example is included to show the applicability of our result.
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Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation
M. Imran,
Madeeha Tahir,
M. A. Imran,
A. U. Awan
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
25-31
Received:
31 May 2015
Accepted:
1 June 2015
Published:
15 June 2015
Abstract: In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of an Oldroyd-B fluid, between two infinite coaxial circular cylinders, are determined by applying the finite Hankel transforms. The motion is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent rotational shear stress. The solutions that have been obtained are presented under series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for Maxwell, second grade and Newtonian fluids are obtained as limiting case of general solutions. Finally, the influence of the pertinent parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.
Abstract: In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of an Oldroyd-B fluid, between two infinite coaxial circular cylinders, are determined by applying the finite Hankel transforms. The motion is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent rotational shear stress...
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On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer
Zermina Gull Bhutta,
M. N. Naeem,
M. Imran
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
32-40
Received:
31 May 2015
Accepted:
1 June 2015
Published:
15 June 2015
Abstract: In the current analysis vibration characteristics of a cylindrical shell composed of three layers are examined. Vibration of cylindrical shells is accomplished for their involvement in various areas of engineering and technology. Shell vibration behavior depends upon on different geometrical material parameters and material parameters. They provide the maximum stability of a physical system. There is graduation distribution of constituent materials in functionally graded materials and is controlled by polynomial, exponential and trigonometric volume exponent fraction laws. In the present study a cylindrical shell is composed of three layers whereas the middle layer consists of functionally graded material and the extreme layer are of isotropic nature. Material composition of the FG layer is governed by polynomial, exponential and trigonometric volume fraction exponent laws. Impact of these laws is examined on shell vibration frequencies for different physical parameters. Love’s thin shell theory is adopted for shell motion equations. The vibration of cylindrical shells with FGM will be expressed by using the Raleigh-Ritz technique in this method. Three volume fraction laws are used to define the middle layer of tri-layer cylindrical shells. The Rayleigh-Ritz technique is applied to form the shell frequency equation which is solved by MATLAB software. The validity and accuracy of this method is investigated for a number of comparisons of numerical results.
Abstract: In the current analysis vibration characteristics of a cylindrical shell composed of three layers are examined. Vibration of cylindrical shells is accomplished for their involvement in various areas of engineering and technology. Shell vibration behavior depends upon on different geometrical material parameters and material parameters. They provide...
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Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
41-45
Received:
30 May 2015
Accepted:
1 June 2015
Published:
15 June 2015
Abstract: In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.
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Generalized Quasi-Variational Inequalities for Pseudo-Monotone Type III and Strongly Pseudo-Monotone Type III Operators on Non-Compact Sets
Mohammad S. R. Chowdhury,
Yeol Je Cho
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
46-53
Received:
5 April 2015
Accepted:
9 April 2015
Published:
17 June 2015
Abstract: In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Chowdhury and Tan’s generalized version [1] of Ky Fan’s minimax inequality [2] as the main tool.
Abstract: In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pse...
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Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions
Naseer Ahmad Asif,
Imran Talib
Issue:
Volume 3, Issue 3-1, June 2015
Pages:
54-59
Received:
17 April 2015
Accepted:
20 April 2015
Published:
17 June 2015
Abstract: We study existence of solution in the presence of upper and lower solutions of some second-order nonlinear coupled ordinary differential system (ODS for short) depending on first order derivatives with nonlinear coupled boundary conditions (CBCs for short). Our method for nonlinear coupled system with nonlinear CBCs is new and it unifies the treatment of many different second order problems. Nagumo condition is used to define bound for the derivative of the solution. Coupled lower and upper solutions, Arzela-Ascoli theorem and Schauder's fixed point theorem play an important role in establishing the arguments.
Abstract: We study existence of solution in the presence of upper and lower solutions of some second-order nonlinear coupled ordinary differential system (ODS for short) depending on first order derivatives with nonlinear coupled boundary conditions (CBCs for short). Our method for nonlinear coupled system with nonlinear CBCs is new and it unifies the treatm...
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