---

In this paper, we investigate Schur-convexity of some functions which are obtained from the co-ordinated convex functions on a rectangular box in `R^3`.

---

In this paper, we  introduce and study a new iterative method which is based on viscosity general algorithm and forward-backward splitting method  for finding a common element of the set of common fixed points of multivalued demicontractive and quasi-nonexpansive mappings and the set of solutions of  variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings in  real Hilbert spaces. We prove that the sequence $x_n$ which is generated by the proposed iterative algorithm converges strongly to a common element of two sets above. Finally, our theorems are applied to approximate a common solution of fixed point problems with set-valued operators and the composite convex minimization problem. Our theorems are significant improvements on several important recent results.

---

‎In this paper‎, ‎we introduce a semi-symmetric non-metric connection on `eta`-Kenmotsu manifolds that changes an `eta`-Kenmotsu manifold into an Einstein manifold‎. ‎Next‎, ‎we consider an especial version of this connection and show that every Kenmotsu manifold is `xi`-projectively flat with respect to this connection‎. ‎Also‎, ‎we prove that if the Kenmotsu manifold `M` is a `xi`-concircular flat with respect to the new connection‎, ‎then `M` is necessarily of zero scalar curvature‎. ‎Then‎, ‎we review the sense of `xi`-conformally flat on Kenmotsu manifolds and show that a `xi`-conformally flat Kenmotsu manifold with respect to the new connection is an `eta`-Einstein with respect to the Levi-Civita connection‎. ‎Finally‎, ‎we prove that there is no `xi`-conharmonically flat Kenmotsu manifold with respect to this connection‎.

---

The finite difference-self consistent field iteration is presented to solve some non-linear eigenvalue differential equations‎.Some properties of the self consistent field iteration and finite difference methods required for our subsequent development are given‎. ‎Numerical examples are included to demonstrate the validity and applicability of the present technique. A comparison is also made with the existing results‎. ‎The method is easy to implement and yields accurate results‎.‎‎

---

In this paper we prove the existence of at least three solutions to the following second-order impulsive system:
 
where `A: [0, T] rightarrow mathbb{R}^{N times N}` is a continuous map from the interval `[0, T]` to the set of `N`-order symmetric matrixes. The approach is fully based on a recent three critical points theorem of Teng [K. Teng, Two nontrivial solutions for hemivariational inequalities driven by nonlocal elliptic operators, Nonlinear Anal. (RWA) 14 (2013) 867-874].

---

In this paper we introduce the concept of mutual entropy map for continuous maps on metric spaces. It is a non-negative extended real number which depends on two measures which are preserved by a system. Then we will extract the Kolmogorov entropy of ergodic systems from the mutual entropy as a special case when the two measures are equal.

---

In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal parity condition of the first kind. We analyze the  completeness,  the basis  property,  and the minimality of the eigenfunctions  in the space `overline(W)_p^(2l) (0,pi)`,  where  `overline(W)_p^(2l) (0,pi)` be the set of functions `f in  W_p^(2l) (0,pi)`, satisfying of the following conditions: `f^{(2k-1)}(0)=0, k=1,2,...,l`.

---

One of the greatest accomplishments in modern financial theory, in terms of both approach and applicability has been the BlackScholes option pricing model. It is widely recognized that the value of a European option can be obtained by solving the Black-Scholes equation. In this paper we use functional perturbation method (FPM) for solving Black-Scholes equation to price a European call option. The FPM is a tool based on considering the differential operator as a functional. The equation is expanded functionally by Frechet series. Then a number of successive partial differential equations (PDEs) are obtained that have constant coefficients and differ only in their right hand side part. Therefore we do not need to resolve the different equations for each step. In contrast to methods that have implicit solutions, the FPM yields a closed form explicit solution.

---

We study variational approximations of a dual pair of mathematical programming problems in terms of epi/hypo-convergence and inside epi/hypo-convergence of approximating Lagrange functions of the pair. First, the Painlevé -Kuratowski convergence of approximate saddle points of approximating Lagrange functions is established under the inside epi/hypo-convergence of these approximating Lagrange functions. From this, we obtain a couple of solutions of the pair of problems and a strong duality. Under a stronger variational convergence called ancillary tight epi/hypo-convergence, we obtain the Painle vé-Kuratowski convergence of approximate minsup-points and approximate maxinf-points of approximating Lagrange functions (when approximate saddle points are not necessary to exist).

---

In this paper, we prove some coupled fixed point theorems for nonlinear contractive mappings which doesn't have the mixed monotone property, in the context of partially ordered `G`-metric spaces. Hence, these results can be applied in a much wider class of problems. Our results improve the result of D. Dori'{c}, Z. Kadelburg and S. Radenovi'{c} [Appl. Math. Lett. (2012)]. We also present two examples to support these new results.

---

In this paper, sufficient conditions ensuring the existence of solutions for set-valued equilibrium problems are obtained. The convexity assumption on the whole domain is not necessary and just the closure of a quasi-self-segment-dense subset of the domain is convex. Using a KKM theorem and a notion of Q-selected preserving $R_{-}^{*}$-intersection
($R_{-}^{*}$-inclusion) for set-valued mapping, the existence results are proved in real Hausdorff topological vector spaces.

---

In this work, the common T approximate strict fixed point property for multi-valued mappings F,G : X -> P_{cl,bd}(X) is introduced to prove necessary and sufficient condition for existence of a common strict xed point of multi-valued mappings involved therein. Our results extend and unify comparable results in the existing literature. We also provide examples to support our results.

 

---

Abstract. Let A, B, and C be Banach algebras, α ∈ Hom(A, B) and β ∈ Hom(C, B), and k α k≤ 1, kβ k≤ 1. IN this paper we define the Banach algebra A×α B×β C by new product on A×B×C which is a strongly splitting extension of C by B. Then we show that these products from a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Finally we consider spectrum, Arens regularity, amenability and weak amenability of these products.

---

 In this paper, we study conformally flat  4-th root (α, β)-metrics on a manifold $M$ of dimension $ngeq3$.  We prove that every conformally flat  4-th root (α, β)-metric with relatively isotropic mean Landsberg curvature must be either Riemannian metrics or locally Minkowski metrics.

 

---

The important issue of the aggregation preference is how to determine the weights associated with different ranking places and DEA models play an important role in this subject. DEA models use assignments of the same aggregate value (equal to unity) to evaluate multiple alternatives as efficient. Furthermore, overly diverse weights can appear, thus, the efficiency of different alternatives obtained by different sets of weights may be unable to be compared and ranked on the same basis. In order to solve two above problems, and rank all the alternatives on the same scale, in this paper, we propose a multiple objective programming (MOP) approach for generating a common set of weights in the DEA framework. Also, we develop a novel model to make a maximum discriminating among candidates’ rankings. Additionally, we present two scenarios to provide suitable strategies for solving the proposed MOP model.

---

In this paper, we develop a numerical method to solve a famous free boundary PDE called the one dimensional Stefan problem.
First, we rewrite the PDE as a variational inequality problem (VIP). Using the linear finite element method, we discretize the variational inequality and achieve a linear complementarity problem (LCP). We present some existence and uniqueness theorems for solutions of the variational inequalities and free boundary problems. Finally we solve the LCP numerically by applying a modification of the active set strategy.

---

In this article, the properties of single-term Walsh series are presented and utilized for solving the nonlinear Volterra-Hammerstein integral equations of second kind. The interval [0;1) is divided tomequal subintervals,mis a positive integer number. The midpoint of each subinterval is chosen as a suitable collocation point. By the method the computations of integral equations reduce into some nonlinear algebraic equations. The method is computationally attractive, and gives a continuous approximate solution. An analysis for the convergence of method is presented.The efficiency and accuracy of the method are demonstrated through illustrative examples. Some comparisons aremade with the existing results.

---

In this paper we introduce `omega`-proximal quasi contraction mapping and best `omega`-proximity point in modular metric spaces. In fact, we show that
every `omega`-proximal quasi contraction mapping has unique best `omega`-proximity point in modular metric spaces. Finally, we give an example to illustrate the applications of our results.

---

We introduce variational inequality problems on 2-inner product spaces and prove several existence results for variational inequalities defined on closed convex sets. Also, the relation between variational inequality problems, best approximation problems and fixed point theory is studied.

---

In this article,  two new fixed point results in the framework of complex-valued rectangular extended $b$-metric space are established. Our results include as special cases, some well-known results in the comparable literature.  We provide nontrivial examples and an existence theorem of  a Fredholm type integral equation to support our assertions and to indicate a usability of the results presented herein.