We demonstrate that if J is an M-ideal in a Lindenstrauss space X, then X satisfies the famous Smith and Ward identity, that is, for finite subsets F of X. We introduce strong property- for a triplet where X is a Banach space, V is a closed convex subset of X, and is a subfamily of closed, bounded subsets of X. We show that for a subspace V, the restricted Chebyshev centre for with respect to the unit ball of V is non-empty if the triplet has the strong property- We demonstrate that for an M-ideal J in a Lindenstrauss space X, the triplet has the strong property- where is the family of compact subsets of X. Some characterizations of the strong property- are given. Similar to the strong -ball property, we show that for a subspace V of X, a triplet has the strong property- if and only if has the property- and the set of restricted Chebyshev centres with respect to the unit ball of V is non-empty for

Based on n-dimensional Euclidean spaces and n-dimensional torus as underlying spaces, we investigate the rate for the norm convergence of the generalized Bochner–Riesz means on homogeneous Triebel–Lizorkin spaces, and establish the equivalence between the rate and the K-functional. Particularly, we show that such equivalence is closely related to the Bochner–Riesz conjecture on homogeneous Triebel–Lizorkin spaces. Thus, we obtain natural extensions of some well-known theorems by Fefferman, Tomas and Stein and by Carleson, Söjlin and Hörmander.

In the present article, we derive some approximation results concerning the order of convergence for a family of Durrmeyer type exponential sampling operators. Further, we improve the rate of approximation by constructing linear combinations of these operators. At the end, we provide a few examples of the kernel functions to which the presented theory can be applied along with the graphical representation.

Using some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for locally optimal solutions of minimax fractional programming problems under the limiting constraint qualification (LCQ). Sufficient conditions for such solutions to the considered problem are also provided by introducing generalized convex functions defined in terms of the limiting subdifferential for locally Lipschitz functions. In addition, some duality results for minimax fractional programming problems are also provided. Finally, by using the obtained results, we derive necessary and sufficient conditions for weak Pareto solutions to the multiobjective semi-infinite fractional optimization problem.

In contrast to symmetric cone optimization, there has no unified framework for non-symmetric cone optimization. One main reason is that the structure of various non-symmetric cone differs case by case. Especially, their boundary conditions are usually mysterious. In this paper, we provide characterizations of boundary conditions on some non-symmetric cones, including p-order cone, ellipsoidal cone, power cone and general closed convex cone. These results will be key bricks for further investigations on non-symmetric cone optimization accordingly.

In this paper we introduce and study two concepts of global well-posedness for set optimization problems in Hausdorff topological vector spaces. Some relationships among these notions and generalized e-well-posedness concept already existent in the literature are established. Sufficient conditions are also given in order to guarantee global well-posedness. Our notions and results extend similar concepts and results established for set optimization problems in metric spaces.

In this paper, we obtain the operational properties of the set (MaxWA, and MinWA) of a set A in the sense of vector optimization and its’ applications to the judgment of the convexity and concavity of a set-valued mapping. By using the separation theorem of convex sets, some minimax theorems of two set-valued mappings have proved in the nonconvex sets. Simultaneously, two examples are given to show our results.

The purpose of this article is to study convergence analysis of quasi-variational inequalities using a projection-type method coupled with inertial extrapolation step. First, we give strong convergence analysis of the sequence of iterates generated by our proposed method to the unique solution of quasi-variational inequality under some mild assumptions. Later, we show that the sequence converges linearly to the unique solution in a special case of choice of parameters. Another contribution in this article is that the inertial factor in our proposed method is allowed to be equal to 1 unlike other previously proposed inertial projection-type method for solving quasi-variational inequalities in the literature where inertial factor is assumed to be bounded away from 1.

The essential importance of the best proximity point theory is that “best proximity point theory” appears in the coincidence of “metric fixed point theory” and “optimization theory.” So finding best proximity points of mappings satisfying different type of contractive conditions in different structures is one of the fascinating research topics. For this, in this article, we first introduce a new type of proximal property of a pair of subsets of a metric space, which we designate as proximal weakly compact pair. After this, we come up with some new type of proximal contractive and proximal cyclic contractive mappings. Then we investigate the existence of best proximity point(s) in these newly originated mappings in the setting of proximal weakly compact pair of subsets in a metric space.

In this paper, hybrid best proximity points for a class of proximally mixed monotone set-valued mappings are discussed. In order to get rid of the fetter of continuity, we introduce the proximally ordered contraction instead of various proximal distance contractions widely applied in recent literatures and present some new existence and iterative approximation theorems of best proximity points for such mappings. Some examples are given to illustrate the advantages of the obtained results.