Journal of Mathematical Extension
Volume:17 Issue: 1, Jan 2023

We consider the multiobjective semi-infinite programming problems with feasible sets defined by equality and inequality constraints, in which the objective and the constraints functions are locally Lipschitz. First, we introduce an Arrow-Hurwitcz-Uzawa type constraint qualification which is based on the Clarke subdifferential. Then, we derive the strong Karush-Kuhn-Tucker type necessary optimality condition for properly efficient solutions of the considered problems.

The aim of this article is to approximate the multiple solutions of the problem of mixed convection in a porous medium on the half-line utilizing the quasilinearization method (QLM) combined with the finite difference method (FDM). For this purpose, at first, we transform the governing nonlinear differential equation to a sequence of linear differential equations via the quasilinearization approach. Then, we provide a sequence of linear algebraic systems by applying the FDM at each iteration to find the approximate solutions of the obtained linear differential equations. Moreover, we present a beneficial scheme to obtain appropriate initial guesses in order to compute both solutions of the problem. The convergence analysis is considered in detail and some numerical results are reported to demonstrate the validity of the proposed iterative method.

This paper was aimed at studying some novel methods of constructing new c-K-g-frames in a Hilbert space H. Some necessary and sufficient conditions were given for some bounded operators on H under which new c-K-g-frames were obtained from the existing ones. Also, the sum of c-K-g-frames were discussed, some of their characterizations were identified, and some bounded operators offered to construct new c-K-g-frames from the old ones.

In this paper, we study the Lk-biharmonic Lorentzian hypersurfaces of the Minkowski 5-space M5 , whose second fundamental form has three distinct eigenvalues. An isometrically immersed Lorentzian hypersurface, x : M4 1 → M5 , is said to be Lk-biharmonic if it satisfies the condition L 2 kx = 0, where Lk is the linearized operator associated to the 1st variation of the mean curvature vector field of order (k + 1) on M4 1 . In the special case k = 0, we have L0 is the well-known Laplace operator ∆ and by a famous conjecture due to Bang-Yen Chen each ∆-biharmonic submanifold of every Euclidean space is minimal. The conjecture has been affirmed in many Riemanian cases. We obtain similar results confirming the Lk-conjecture on Lorentzian hypersurfaces in M5 with at least three principal curvatures.

We investigate the existence and uniqueness of the solution and also the rate of convergence of a numerical method for a fractional differential equation in both q-calculus and (p, q)-calculus versions. We use the Banach and Schauder fixed point theorems in this study. We provide two examples, one by definition of the q-derivative and the other by (p, q)-derivative. We compare the rate of convergence of the numerical method. We like to clear some facts on (p, q)-calculus. The data from our numerical calculations show well that q-calculus works better than (p, q)-calculus in each case.

This paper considers the notion of α-strong dominating set based on fuzzy bridges in fuzzy graphs and computes the domination number of wheel fuzzy graphs and complete (multi) partite fuzzy graphs. In this regard, we consider the fuzzy cycles and compute the domination number of wheel fuzzy graphs, supremum center-based wheel fuzzy graph, infimum center-based wheel fuzzy graph, and complete (multi) partite fuzzy graphs with any given fuzzy vertices. It investigated the relationship between the domination number of wheel fuzzy graphs and complete (multi) partite fuzzy graphs via some critical fuzzy vertices in these classes of fuzzy graphs. The new conception of domination number of wheel fuzzy graphs and complete (multi)partite fuzzy graphs based on fuzzy bridges, was given for the first time in this paper and we found an Algorithm in this regard. In the final, we apply the domination number of fuzzy graphs in modeling of real problems of complex networks. AMS Sub

The aim of the paper is to establish the global well-posedness of the Newell-Whitehead-Segel Equation driven by the biharmonic operator with Dirichlet boundary conditions through the semigroup method based on the Hille-Yosida Theorem. In particular, using the blow-up criterion we first demonstrate that there exists a unique local maximal classical solution. Next, by showing that the semiflow generated is uniformly bounded in H4 -norm, it has been that the solution is indeed global in time.

In this paper, we prove some existence and uniqueness results for some classes of deformable implicit fractional differential equations in b-Metric spaces with initial conditions. We base our arguments on some some fixed point theorems. Finally, we provide an example to illustrate our results.

The paper aims is to discuss strong and ∆−convergence of modified k-iteration method in CAT(κ) space, where κ > 0, for nearly asymptotically nonexpansive mappings. Our results generalize the corresponding results of Hussain et al. [10] and Ullah et al. [21].

In the present paper, we propose a numerical method based on the combination of the fixed point method and quadrature formula for solving two-dimensional nonlinear Fredholm integral equations of the second kind. Using uniform and partial modulus of continuity, the error estimation is given. Also, the numerical stability with respect to the choice of the first iteration is proved. Moreover, the accuracy of the method and the correctness of the theoretical results are shown by some examples.