Papers by Mohsen Rostamian Delavar
Mathematical Inequalities & Applications, 2017
Journal of Mathematical Inequalities, 2016
This paper deals with some results in generalized convex spaces. The notion of minimal generalize... more This paper deals with some results in generalized convex spaces. The notion of minimal generalized convex space is introduced and then two well known results in nonlinear analysis, that is the open and closed versions of Fan-KKM principle in this new setting are considered. Indeed, it is shown that, for any m-closed(m-open) valued KKM map F : D X in a minimal generalized convex space (X, D, Γ), {F (z) : z ∈ D} has the finite intersection property. 0 Received .
In this paper we introduce and study a new topology related to a self mapping on a nonempty set. ... more In this paper we introduce and study a new topology related to a self mapping on a nonempty set. Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets of X related to f , i.e. τ f := {A ⊆ X : f (A) ⊆ A} ⊆ P(X) is a topology on X. Among other things, we find the smallest open sets contains a point x ∈ X. Moreover, we find the relations between f and τ f . For instance, we find the conditions on f to show that whenever τ f is T 0 , T 1 or T 2 .
In this paper, the notion of maximal m-open set is introduced and its properties are investigated... more In this paper, the notion of maximal m-open set is introduced and its properties are investigated. Some results about existence of maximal m-open sets are given. Moreover, the relations between maximal m-open sets in an m-space and maximal open sets in the corresponding generated topology are considered. Our results are supported by examples and counterexamples.
This paper deals with some fixed point and maximal element theorems via transfer closed, KKM mult... more This paper deals with some fixed point and maximal element theorems via transfer closed, KKM multimaps in minimal generalized convex spaces. Moreover, some generalized versions of Fan-KKM principle for transfer closed multimaps are given. Nonlinear
At the present paper, by using Fan-KKM principle in minimal generalized convex spaces, a minimax ... more At the present paper, by using Fan-KKM principle in minimal generalized convex spaces, a minimax inequality of Ky Fan is proved. Also, Fan's well known two-functions minimax inequality in this new setting is given. 0
In this paper, we investigate the Hyers-Ulam stability of the Tribonacci functional equation
Using some concepts in MKKM space, we prove the generalized forms of open and closed versions of ... more Using some concepts in MKKM space, we prove the generalized forms of open and closed versions of Fan's matching theorem. The S -weakly KKM multimap is applied to obtain a type of KKM theorem. As an application, a Fan type minimax theorem is proved. Moreover, a minimax inequality is given in these new settings.
This paper deals with maximal m-open sets. The m-closure and the m-interior of maximal m-open set... more This paper deals with maximal m-open sets. The m-closure and the m-interior of maximal m-open sets and their properties are investigated. Further, the behaviors of maximal m-open sets in m-homeomorphic m-spaces and product m-spaces are inspected. Our results are supported by some examples and counterexamples.
In this paper, we deal with the notion of abstract convex spaces via minimal spaces as an extende... more In this paper, we deal with the notion of abstract convex spaces via minimal spaces as an extended version of other forms of convexity and establish some well-known results such as coincidence theorems for the classes m-KKM and ms-KKM of multimaps and Ky Fan's type minimax inequality. Mathematics Subject Classification : 26A51; 26B25; 54H25; 55M20; 47H10; 54A05.
This paper deals with coincidence and fixed point theorems in minimal generalized convex spaces. ... more This paper deals with coincidence and fixed point theorems in minimal generalized convex spaces. By establishing a kind of KKM Principle in minimal generalized convex space, we obtain some results on coincidence point and fixed point theorems. Generalized versions of Ky Fan's lemma, Fan-Browder fixed point theorem, Nash equilibrium theorem and some Urai's type fixed point theorems in minimal generalized convex spaces are given.
This paper is devoted to introduce the concepts of transfer closed and transfer open multimaps in... more This paper is devoted to introduce the concepts of transfer closed and transfer open multimaps in minimal spaces. Also, some characterizations of them are considered. Further, the notion of minimal local intersection property will be introduced and characterized. Moreover, some maximal element theorems via minimal transfer closed multimaps and minimal local intersection property are given. (M. Alimohammady), [email protected] (M. Roohi), [email protected] (M.R. Delavar).
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Papers by Mohsen Rostamian Delavar