Bulletin of The Iranian Mathematical Society, 2017
In this paper, some properties of pre-monotone operators are proved. It is shown that in a r... more In this paper, some properties of pre-monotone operators are proved. It is shown that in a reflexive Banach space, a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous. The notion of $sigma$-convexity is introduced and the relations between the $sigma$-monotonicity and $sigma$-convexity is investigated. Moreover, some results on the sum and difference of two $sigma$-monotone operators is considered.
This paper is devoted to consider the notions of complementary problem (CP) and set-valued comple... more This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. Our results illustrated by some examples. This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the s...
This paper deals with fixed point theory and fixed point property in minimal spaces. We will prov... more This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X such that both x and f(x) belong to a common Bα. Further, it is shown that if (X,M) has the fixed point property, then its minimal retract subset enjoys this property.
Journal of Applied Mathematics and Stochastic Analysis, 2006
Here, we would study and characterize fuzzy ϕψ-continuity for fuzzy multifunctions which extend f... more Here, we would study and characterize fuzzy ϕψ-continuity for fuzzy multifunctions which extend fuzzy ϕψ-continuity of fuzzy functions. Moreover, we obtain some results in fuzzy multifunctions.
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2020
In the present paper, monotone relations and maximal monotone relations from an Hadamard space to... more In the present paper, monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are investigated. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced. It is shown that Fitzpatrick transform of a special class of monotone relations is proper, convex and lower semi-continuous. Finally, a representation result for monotone relations is given.
In this paper, we introduce a composite iterative method for finding a common zero point of weigh... more In this paper, we introduce a composite iterative method for finding a common zero point of weighted resolvent average of a finite family of monotone operators. Furthermore, the strong convergence of the proposed iterative method is established. Finally, our results are illustrated by some numerical examples.
In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, whe... more In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, where X is an Hadamard space and X? is its linear dual space. It is shown that an Hadamard space X is flat if and only if X x X? has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. A characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is given. Finally, a type of Debrunner-Flor Lemma concerning extension of monotone relations in Hadamard spaces is proved.
Abstract. At the present paper, the notions of induced fuzzy minimal structures, fuzzy minimal su... more Abstract. At the present paper, the notions of induced fuzzy minimal structures, fuzzy minimal subspaces and relatively fuzzy minimal continuous functions are introduced and studied. AMS Mathematics Subject Classification (2000): Primary 54A40, Secondary 03E72, 54A05. ...
In this paper we prove some fixed points results on cone metric spaces for maps satisfying genera... more In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen [11] from metric spaces to cone metric spaces. The example is included.
This paper deals with hyper metric spaces as a generalization of metric spaces. Hyper convergent ... more This paper deals with hyper metric spaces as a generalization of metric spaces. Hyper convergent sequence, hyper continuous function and hyper contraction map are introduced and some results in these settings are investigated. In particular, it is found that any hyper contraction map on a hyper metric space (X,D) has a unique fixed point. Finally, Cantor’s theorem and the Baire category theorem in hyper metric space are given.
This note deals with Markov-Kakutani’s fixed point theorem with respect to a compact p-star shape... more This note deals with Markov-Kakutani’s fixed point theorem with respect to a compact p-star shaped subset of a topological vector space. It is proved that every commutative family of continuous p-affine self mappings on a compact p-star shaped subset of a topological vector space has a common fixed point.
Bulletin of The Iranian Mathematical Society, 2017
In this paper, some properties of pre-monotone operators are proved. It is shown that in a r... more In this paper, some properties of pre-monotone operators are proved. It is shown that in a reflexive Banach space, a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous. The notion of $sigma$-convexity is introduced and the relations between the $sigma$-monotonicity and $sigma$-convexity is investigated. Moreover, some results on the sum and difference of two $sigma$-monotone operators is considered.
This paper is devoted to consider the notions of complementary problem (CP) and set-valued comple... more This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. Our results illustrated by some examples. This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the s...
This paper deals with fixed point theory and fixed point property in minimal spaces. We will prov... more This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X such that both x and f(x) belong to a common Bα. Further, it is shown that if (X,M) has the fixed point property, then its minimal retract subset enjoys this property.
Journal of Applied Mathematics and Stochastic Analysis, 2006
Here, we would study and characterize fuzzy ϕψ-continuity for fuzzy multifunctions which extend f... more Here, we would study and characterize fuzzy ϕψ-continuity for fuzzy multifunctions which extend fuzzy ϕψ-continuity of fuzzy functions. Moreover, we obtain some results in fuzzy multifunctions.
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2020
In the present paper, monotone relations and maximal monotone relations from an Hadamard space to... more In the present paper, monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are investigated. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced. It is shown that Fitzpatrick transform of a special class of monotone relations is proper, convex and lower semi-continuous. Finally, a representation result for monotone relations is given.
In this paper, we introduce a composite iterative method for finding a common zero point of weigh... more In this paper, we introduce a composite iterative method for finding a common zero point of weighted resolvent average of a finite family of monotone operators. Furthermore, the strong convergence of the proposed iterative method is established. Finally, our results are illustrated by some numerical examples.
In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, whe... more In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, where X is an Hadamard space and X? is its linear dual space. It is shown that an Hadamard space X is flat if and only if X x X? has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. A characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is given. Finally, a type of Debrunner-Flor Lemma concerning extension of monotone relations in Hadamard spaces is proved.
Abstract. At the present paper, the notions of induced fuzzy minimal structures, fuzzy minimal su... more Abstract. At the present paper, the notions of induced fuzzy minimal structures, fuzzy minimal subspaces and relatively fuzzy minimal continuous functions are introduced and studied. AMS Mathematics Subject Classification (2000): Primary 54A40, Secondary 03E72, 54A05. ...
In this paper we prove some fixed points results on cone metric spaces for maps satisfying genera... more In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen [11] from metric spaces to cone metric spaces. The example is included.
This paper deals with hyper metric spaces as a generalization of metric spaces. Hyper convergent ... more This paper deals with hyper metric spaces as a generalization of metric spaces. Hyper convergent sequence, hyper continuous function and hyper contraction map are introduced and some results in these settings are investigated. In particular, it is found that any hyper contraction map on a hyper metric space (X,D) has a unique fixed point. Finally, Cantor’s theorem and the Baire category theorem in hyper metric space are given.
This note deals with Markov-Kakutani’s fixed point theorem with respect to a compact p-star shape... more This note deals with Markov-Kakutani’s fixed point theorem with respect to a compact p-star shaped subset of a topological vector space. It is proved that every commutative family of continuous p-affine self mappings on a compact p-star shaped subset of a topological vector space has a common fixed point.
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