In this paper, two generalized contractions, the generalized F t s -contraction and the generalized (, , F t s )-contraction, are introduced.Two fixed point theorems were established in ordered b-metric spaces.An example is presented for illustrating the fixed point theorem of the generalized F t s -contraction.

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This paper is concerned with the semi-infinite programming problems with vanishing constraints. Both necessary and sufficient Karush-Kuhn-Tucker optimality conditions for the semi-infinite programming problems with vanishing constraints are established. We also formulate types of Wolfe and Mond-Weir dual problems and explore duality relations under convexity assumptions. Some examples are given to illustrate our results.

In this paper, with the aid of square quadratic proximal (SQP) method and the self-adaptive adjustment rule, we propose an SQP alternating direction method for solving the linearly constrained separable convex programming with three separable operators. Under standard assumptions, the global convergence of the proposed method is proved. Its efficiency is also verified via some numerical experiments.

The paper deals with the study of tensor variational inequalities. and some projection methods to solve them. In particular, some properties on the solutions to such an inequality are established and a fixed point theorem is proved. Moreover, some numerical methods are introduced and the convergence analysis of them is investigated. All the theoretical results are applied to analyze a general oligopolistic market equilibrium problem in which each firm produces several commodities and has some production excesses since the equilibrium condition is characterized by means of a tensor variational inequality. A numerical example is also discussed.

In this paper, we combine variational methods and truncation techniques to study the existence of at least two weak solutions for a p-Laplacian problem depending by a positive parameter and with reaction term singular at zero. A quantitative estimate of the parameters is also given.

The aim of this paper is to present some local fixed point results for graphic contractions in complete metric spaces.

In this paper, a new nonlinear mapping, which is said to be further 2-generalized hybrid, is introduced. The new mapping includes further generalized hybrid and normally 2-generalized hybrid mappings as special cases. A Halpern-type iterative scheme is constructed for attractive points of further 2-generalized hybrid mappings in a complete CAT(0) space.

In this paper, we propose a simultaneous projected subgradient-proximal type iterative algorithm to solve a split equality equilibrium problem with pseudomonotone bifunctions in 2-uniformly convex and uniformly smooth Banach spaces. We obtain convergence results under some mild conditions on the bifunctions. Furthermore, we also give applications to the domain decomposition for PDEs.

The aim of this paper is to introduce an iterative process for a common solution of fixed point problem of a continuous pseudocontractive mapping, a variational inequality problem and an equilibrium problem provided their common solution exists. Moreover, a numerical example which supports our main convergence results is presented.