Fixed points of regular set-valued mappings in quasi-metric spaces

Positive L^TP and Continuous Solutions for Fredholm Integral Inclusions. A Note on the Structure of the Solution Set for the Cauchy Differential Inclusion in Banach Spaces. Fixed Point Theory for Acylic Maps between Topological Vector Spaces having Sufficiently many Linear Functionals, and Generalized Contractive Maps with Closed Values between Complete Metric Spaces. Using the Integral Manifolds to Solvability of Boundary Value Problems. On the Semicontinuity of Nonlinear Spectra. Existence Results for Two-Point Boundary Value Problems. Generalized Strongly Nonlinear Implicit Quasi-Variational Inequalities for Fuzzy Mappings. Vector Variational Inequalities, Multi-Objective Optimizations, Pareto Optimality and Applications. Variational Principle and Fixed Points. On the Baire Category Method in Existence Problems for Ordinary and Partial Differential Inclusions. Maximal Element Principles on Generalized Convex Spaces and their Applications. Fixed Point Results for Multi-valued Contractions on Gauge Spaces. The Study of Variational Inequalities and Applications to Generalized Complementarity Problems, Fixed Point Theorems of Set-Valued Mappings and Minimization Problems. Remarks on the Existence of Maximal Elements with Respect to a Binary Relation in Non-Compact Topological Spaces. Periodic Solutions of a Singularly Perturbed System of Differential Inclusions in Banach Space. Constrained Differential Inclusions. Nonlinear Boundary Value Problems with Multi-valued Terms. Optimal Control of a Class of Nonlinear Parabolic Problems with Multi-valued Terms. Continuation Theory for A-Proper Mappings and their Uniform Limits and Nonlinear Perturbations of Fredholm Mappings. Existence Theorems for Strongly Accretive Operators in Banch Spaces. A Kneser Type Property for the Solution Set of a Semilinear Differential Inclusion with Lower Semicontinuous Nonlinearity. A Nonlinear Multi-valued Problem with Nonlinear Boundary Conditions. Extensions of Monotone Sets. Convergence of Iterates of Nonexpansive Set-Valued Mappings. A Remark on the Intersection of a Lower Semicontinuous Multi-function and Fixed Set. Random Approximations and Random Fixed Point Theorems for Set-Valued Random Maps.Existence Theorems for Two-Variable Functions and Fixed Point Theorems for Set-Valued Mappings. An Extension Theorem and Duals of Gale-Mas-Colell's and Shafer-Sonnenschein's Theorems. Iterative Algorithms for Nonlinear Variational Inequalities Involving Set-Valued H-Cocoercive Mappings.

In this paper, we introduce the concept of a generalized weak contraction for set-valued mappings defined on quasi-metric spaces. We show the existence of fixed points for generalized weakly contractive set-valued mappings. Indeed, we have a generalization of Nadler’s fixed point theorem and Banach’s fixed point theorem in quasi-metric spaces and, further, investigate the convergence of iterate scheme of the form xn+1 ∈ Fxn with error estimates.

Common fixed point theorems and variational principle in generating spaces of quasi-metric family

In this work, several fixed point theorems of set-valued monotone mappings and set-valued Caristi-type mappings are proved in partially ordered Hausdorff topological spaces, which indeed extend and improve many recent results in the setting of metric spaces.

Fixed point theorems for fuzzy mappings in complete metric spaces

The aim of this thesis is twofold. On the one hand new results on the concavity and the isotonicity of the optimal solution function of a parametric maximization problem are obtained. The maximizing function is not required to be continuous and the generalized version of the notion of pseudoconcavity in terms of Dini derivatives is used. These results, together with a new fixed point theorem for set-valued maps, are used to answer to the second issue concerning a selection of Nash equilibria, called equilibrium under passive beliefs, of a multi-leader multi-follower game with vertical separation and partially observed actions. Indeed, an equilibrium under passive beliefs correspond to a fixed point of particular set-valued maps related to the sets of solutions of parametric bilevel optimization problems. Existence of equilibria under passive beliefs for significative classes of problems and conditions of minimal character on data possibly discontinuous are proved. An economic example of such interaction can be found in games of multilateral vertical contracts: competing manufacturers (the leaders) delegate retail decisions to exclusive retailers (the followers), offering a private contract.

Best approximation, coincidence and fixed point theorems for set-valued maps in [formula omitted]-trees

Caristi's fixed point theorem for fuzzy mappings and Ekeland's variational principle

This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory.

This paper extends the concept of cone subconvexlikeness of single-valued maps to set-valued maps and presents several equivalent characterizations and an alternative theorem for cone-subconvexlike set-valued maps. The concept and results are then applied to study the Benson proper efficiency for a vector optimization problem with set-valued maps in topological vector spaces. Two scalarization theorems and two Lagrange multiplier theorems are established. After introducing the new concept of proper saddle point for an appropriate set-valued Lagrange map, we use it to characterize the Benson proper efficiency. Lagrange duality theorems are also obtained

We provide a new definitions of multivalued metric as well as we developing some fixed point theorems for set-valued maps inpartially D* - space by making use of implicit-relation with example.

We prove a related fixed point theorem for set-valued mappings in three Menger spaces. Some examples are also furnished to support the results. Our main result generalizes and extends several known results in the literature.

In this paper, we provide coincidence point and fixed point theorems satisfying an implicit relation, which extends and generalizes the result of Gregori and Sapena, for set-valued mappings in complete partially ordered fuzzy metric spaces. Also we prove a fixed point theorem for set-valued mappings on complete partially ordered fuzzy metric spaces which generalizes results of Mihet and Tirado. MSC:54E40, 54E35, 54H25.

This is the first part of a work on generalized variational inequalities and their applications in optimization. It proposes a general theoretical framework for the solvability of variational inequalities with possibly non-convex constraints and objectives. The framework consists of a generic constrained nonlinear inequality ( $\exists\hat{u}\in\Psi(\hat {u})$ , $\exists \hat{y}\in\Phi(\hat{u})$ , with $\varphi(\hat{u},\hat{y},\hat{u})\leq \varphi(\hat{u},\hat{y},v)$ , $\forall v\in\Psi(\hat{u})$ ) derived from new topological fixed point theorems for set-valued maps in the absence of convexity. Simple homotopical and approximation methods are used to extend the Kakutani fixed point theorem to upper semicontinuous compact approachable set-valued maps defined on a large class of non-convex spaces having non-trivial Euler-Poincare characteristic and modeled on locally finite polyhedra. The constrained nonlinear inequality provides an umbrella unifying and extending a number of known results and approaches in the theory of generalized variational inequalities. Various applications to optimization problems will be presented in the second part to this work to be published ulteriorly.

Let \(\Phi \) be the class of all real functions \(\varphi : [0, \infty [ \times [0, \infty [ \rightarrow [0, \infty [\) that satisfy the following condition: there exists \(\alpha \in ]0, 1[ \text { such that } \varphi ((1 - \alpha ) r, \alpha r) 0\). In this paper, we show that if X is a nonempty compact convex subset of a real normed vector space, any two closed set-valued mappings \(T, S: X \rightrightarrows X\), with nonempty and convex values, have a common fixed point whenver there exists a function \(\varphi \in \Phi \) such that $$\begin{aligned} \Vert y - u\Vert \le \varphi (\Vert y - x\Vert , \Vert u - x\Vert ), \; \text { for all } x\in X, y\in T(x), u\in S(x). \end{aligned}$$ Next, we prove that the same conclusion holds when at least one of the set-valued mappings is lower semicontinuous with nonempty closed and convex values. Our common fixed point theorems turn out to be useful for a unitary treatment of several problems from optimization and nonlinear analysis (quasi-equilibrium problems, quasi-optimization problems, constrained fixed point problems, quasi-variational inequalities).