Papers by Hamid Reza Hajisharifi
A fixed point theorem for generalized nonexpansive mappings
Miskolc Mathematical Notes
In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. ... more In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-continuous L-type mappings and upper semi-continuous quasi-nonexpansive mappings. We study relationships between MD-type mappings and some other set-valued generalization of nonexpansive mappings. In the sequel we show that if E is a nonempty, weakly compact and convex subset of a Banach space (X,‖.‖) for which every D-type self-mapping on E has a fixed point, then every MD-type self-mapping on E has a fixed point. This result gives a partial affirmative answer to an open problem of Rich. Moreover, we establish some fixed theorems for MD-type mappings which generalize some well-known results in t...
Bulletin of the Iranian Mathematical Society, 2019
In this article, we introduce the concepts of multivalued (DL)-type and multivalued α-nonexpansiv... more In this article, we introduce the concepts of multivalued (DL)-type and multivalued α-nonexpansive mappings in the Banach spaces. We show that these two classes of mappings properly contain some important classes of nonlinear mappings. Moreover, we compare the relationship between such classes of mappings and obtain some fixed point results. In addition, we give partial answer to the open question posed by Reich in 1983, about the relationship between fixed point property of multivalued and singlevalued nonexpansive mappings. This contribution generalizes and improves some recent results in this context.
Journal of Global Optimization, 2019
In this paper, we characterize the nonemptiness of the set of weak minimal elements for a nonempt... more In this paper, we characterize the nonemptiness of the set of weak minimal elements for a nonempty subset of a linear space. Moreover, we obtain some existence results for a nonconvex set-valued optimization problem under weaker topological conditions. Keywords Algebraic interior • Linear space • Set-valued optimization • Vector closure 1 Introduction and preliminaries Let Y be a real linear space ordered by a convex cone C ⊆ Y which is assumed to be proper; i.e., {0} = C = Y. Let K be a nonempty set and F : K ⇒ Y be a set-valued mapping with nonempty values. A general form of set-valued optimization problem is usually defined as follows: (SOP) min F(x) subject to x ∈ K. There are two approaches to defining the solutions of this problem: the vector approach [3,14,17] and the set approach [15,16]. In the vector approach,x ∈ K is a solution of the problem (SOP), whenever F(x) contains a weak minimal element or minimal element of F(K) = ∪ x∈K F(x). In the set approach, it is necessary to introduce an ordering for sets and find a minimal element of subset {F(x) : x ∈ K } of P(Y), where P(Y) is the set of B M. Fakhar
Some Generalizations of the Weierstrass Theorem
SIAM Journal on Optimization, 2016
The main goal of this paper is to obtain a generalization of the Weierstrass theorem for transfer... more The main goal of this paper is to obtain a generalization of the Weierstrass theorem for transfer weakly lower continuous functions on noncompact topological spaces. To achieve this goal, the notion of a quasi-regular-global-inf (qrgi) function on a topological space is introduced, some equivalent statements are given, and a Weierstrass-type theorem for such functions is proved. Moreover, the well-posedness of the minimization problem for regular-global-inf (rgi) and qrgi functions is studied. Furthermore, in the setting of reflexive Banach spaces the existence of global minimum points of noncoercive qrgi and transfer weakly lower continuous functions are investigated. We also introduce the concept of nearly quasi-convexity of a function, as a generalization of the quasi-convexity notion, and present a result on the minimization problem of these functions.
Fixed Point Theory and Applications, 2013
In this paper, we first introduce two new classes of ( ω , δ ) -contractions of the first and sec... more In this paper, we first introduce two new classes of ( ω , δ ) -contractions of the first and second kinds and establish some related new fixed point and best proximity point theorems in preordered metric spaces. Our theorems subsume the corresponding recent results of Samet (J. Optim. Theory Appl. (2013), doi:10.1007/s10957-013-0269-9) and extend and generalize many of the well-known results in the literature. An example is also provided to support our main results. MSC: 47H10, 41A65.
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Papers by Hamid Reza Hajisharifi