Reza Saadati - Academia.edu (original) (raw)

Papers by Reza Saadati

Chaos Solitons & Fractals, 2009

Recently, Lael and Nourouzi [Some results on the IF-normed spaces. Chaos, Solitons & Fractals... more Recently, Lael and Nourouzi [Some results on the IF-normed spaces. Chaos, Solitons & Fractals 2006; doi:10.1016/j.chaos.2006.10.019] introduced and studied a new notation of IF-normed spaces by using the idea of intuitionistic fuzzy normed spaces due to Saadati and Park [On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals 2006;27:331–44], a special continuous t-norm i.e. min and a special continuous s-norm i.e. max. In this note, we consider the modified definition of IF-normed space i.e. LF-normed spaces and prove the open mapping and closed graph theorems for this space using arbitrary continuous t-norm.

Journal of Applied Mathematics and Computing, 2005

The main aim of this paper is to consider the fuzzy norm, difine the fuzzy Banach spaces, its quo... more The main aim of this paper is to consider the fuzzy norm, difine the fuzzy Banach spaces, its quotients and prove some theoremes and in particular Open mapping and Closed graph theoremes on these spaces.

Journal of Inequalities and Applications, 2008

Journal of Applied Sciences, 2009

ABSTRACT In this study, the stability of the cubic functional equation: f(2x+y)+f(2x-y) = 2f(x+y)... more ABSTRACT In this study, the stability of the cubic functional equation: f(2x+y)+f(2x-y) = 2f(x+y)+2f(x-y)+ 12f(x) in the setting of Menger probabilistic normed spaces is proved.

Computers & Mathematics With Applications, 2009

In this paper, several integral equations are solved by He's variational iteration method in gene... more In this paper, several integral equations are solved by He's variational iteration method in general case, then we consider the convergence of He's variational iteration method for solving integral equations.

Applied Mathematics and Computation, 2008

In this paper first we prove a common fixed point theorem in Menger probabilistic metric spaces. ... more In this paper first we prove a common fixed point theorem in Menger probabilistic metric spaces. Then we present a nonlinear contraction case of Jungck's common fixed point theorem in Menger probabilistic metric spaces. Finally, we prove a common fixed point theorem for six self-maps in a Menger probabilistic metric space.

Topology and Its Applications, 2009

In this paper, a concept of monotone generalized contraction in partially ordered probabilistic m... more In this paper, a concept of monotone generalized contraction in partially ordered probabilistic metric spaces is introduced and some fixed and common fixed point theorems are proved. Presented theorems extend the results in partially ordered metric spaces of Nieto and Rodriguez-Lopez [Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223–239; Existence and

Chaos Solitons & Fractals, 2009

In this paper, we consider complete probabilistic metrizable (topological) space and prove that a... more In this paper, we consider complete probabilistic metrizable (topological) space and prove that any G d set in a complete probabilistic metric spaces is a topologically complete probabilistic metrizable space.

We improve Park and Bae's common fixed point the- orem which ... more We improve Park and Bae's common fixed point the- orem which is a generalization of Meir and Keeler's fixed point theorem. We extend Kannan's fixed point theorem to a common fixed point theorem of two commuting maps. Also, using the notion of biased mappings, we prove another common fixed point theorem.

Chaos Solitons & Fractals, 2007

We give some new definitions of D * -metric spaces and we prove a common fixed point theorem for ... more We give some new definitions of D * -metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete D * -metric spaces. We get some improved versions of several fixed point theorems in complete D * -metric spaces.

Journal of Mathematical Analysis and Applications, 2008

In this paper, we consider strongly bounded linear operators on a finite dimensional probabilisti... more In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete.

Acta Applicandae Mathematicae, 2010

The main problem analyzed in this paper consists in showing that, under some conditions, every al... more The main problem analyzed in this paper consists in showing that, under some conditions, every almost quartic mapping from a linear space to a random normed space under the Łukasiewicz t-norm can be suitably approximated by a quartic function, which is unique.

Mathematical and Computer Modelling, 2010

In this paper, we consider the concept of a Ω-distance on a complete partially ordered G-metric s... more In this paper, we consider the concept of a Ω-distance on a complete partially ordered G-metric space and prove some fixed point theorems.

Chaos Solitons & Fractals, 2008

In this paper, we consider complete Menger probabilistic quasi-metric space and prove a common fi... more In this paper, we consider complete Menger probabilistic quasi-metric space and prove a common fixed point theorem for commuting maps in this space.

Journal of Computational and Applied Mathematics, 2009

Keywords: Domain of words Quicksort algorithms Intuitionistic fuzzy metric spaces Completeness Fi... more Keywords: Domain of words Quicksort algorithms Intuitionistic fuzzy metric spaces Completeness Fixed point theorem a b s t r a c t

Applied Mathematics and Computation, 2006

The purpose of this paper is to utilize the property (E.A.) and the common property (E.A.) to pro... more The purpose of this paper is to utilize the property (E.A.) and the common property (E.A.) to prove some existence results on common fixed point for contractive mappings in fuzzy metric spaces which include fuzzy metric spaces of two types, namely, Kramosil and Michalek fuzzy metric spaces along with George and Veeramani fuzzy metric spaces. Our results generalize and extend several relevant common fixed point theorems from the literature. We also furnish an illustrative example.

Chaos Solitons & Fractals, 2008

Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073-9] proved some fixe... more Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073-9] proved some fixed point theorems in intuitionistic fuzzy metric spaces by a strong definition of Cauchy sequence (see [George and Veeramani, Fuzzy Sets Syst 1994;64:395-9] and [Veeramani and Vasuki, Fuzzy Sets Syst 2003;135:409-13]), also the intuitionistic fuzzy metric space has extra conditions (see [Gregori et al., Chaos, Solitons & Fractals, 2006;28:902-5]). In this paper, we consider generalized intuitionistic fuzzy metric spaces i.e., L-fuzzy metric spaces and prove the fuzzy version of Banach and Edelstein contraction theorems in these spaces for modified definition of Cauchy sequence.

Chaos Solitons & Fractals, 2008

Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Ve... more Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new.

Computers & Mathematics With Applications, 2010

Lee et al. considered the following quadratic functional equation f(lx+y)+f(lx−y)=2l2f(x)+2f(y) a... more Lee et al. considered the following quadratic functional equation f(lx+y)+f(lx−y)=2l2f(x)+2f(y) and proved the Hyers–Ulam–Rassias stability of the above functional equation in classical Banach spaces.In this paper, we prove the Hyers–Ulam–Rassias stability of the above quadratic functional equation in non-Archimedean L-fuzzy normed spaces.

Applied Mathematics Letters, 2010

In this work, we prove the generalized Hyers-Ulam stability of the following functional inequality:

Chaos Solitons & Fractals, 2009

Recently, Lael and Nourouzi [Some results on the IF-normed spaces. Chaos, Solitons & Fractals... more Recently, Lael and Nourouzi [Some results on the IF-normed spaces. Chaos, Solitons & Fractals 2006; doi:10.1016/j.chaos.2006.10.019] introduced and studied a new notation of IF-normed spaces by using the idea of intuitionistic fuzzy normed spaces due to Saadati and Park [On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals 2006;27:331–44], a special continuous t-norm i.e. min and a special continuous s-norm i.e. max. In this note, we consider the modified definition of IF-normed space i.e. LF-normed spaces and prove the open mapping and closed graph theorems for this space using arbitrary continuous t-norm.

Journal of Applied Mathematics and Computing, 2005

The main aim of this paper is to consider the fuzzy norm, difine the fuzzy Banach spaces, its quo... more The main aim of this paper is to consider the fuzzy norm, difine the fuzzy Banach spaces, its quotients and prove some theoremes and in particular Open mapping and Closed graph theoremes on these spaces.

Journal of Inequalities and Applications, 2008

Journal of Applied Sciences, 2009

ABSTRACT In this study, the stability of the cubic functional equation: f(2x+y)+f(2x-y) = 2f(x+y)... more ABSTRACT In this study, the stability of the cubic functional equation: f(2x+y)+f(2x-y) = 2f(x+y)+2f(x-y)+ 12f(x) in the setting of Menger probabilistic normed spaces is proved.

Computers & Mathematics With Applications, 2009

In this paper, several integral equations are solved by He's variational iteration method in gene... more In this paper, several integral equations are solved by He's variational iteration method in general case, then we consider the convergence of He's variational iteration method for solving integral equations.

Applied Mathematics and Computation, 2008

In this paper first we prove a common fixed point theorem in Menger probabilistic metric spaces. ... more In this paper first we prove a common fixed point theorem in Menger probabilistic metric spaces. Then we present a nonlinear contraction case of Jungck's common fixed point theorem in Menger probabilistic metric spaces. Finally, we prove a common fixed point theorem for six self-maps in a Menger probabilistic metric space.

Topology and Its Applications, 2009

In this paper, a concept of monotone generalized contraction in partially ordered probabilistic m... more In this paper, a concept of monotone generalized contraction in partially ordered probabilistic metric spaces is introduced and some fixed and common fixed point theorems are proved. Presented theorems extend the results in partially ordered metric spaces of Nieto and Rodriguez-Lopez [Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223–239; Existence and

Chaos Solitons & Fractals, 2009

In this paper, we consider complete probabilistic metrizable (topological) space and prove that a... more In this paper, we consider complete probabilistic metrizable (topological) space and prove that any G d set in a complete probabilistic metric spaces is a topologically complete probabilistic metrizable space.

We improve Park and Bae's common fixed point the- orem which ... more We improve Park and Bae's common fixed point the- orem which is a generalization of Meir and Keeler's fixed point theorem. We extend Kannan's fixed point theorem to a common fixed point theorem of two commuting maps. Also, using the notion of biased mappings, we prove another common fixed point theorem.

Chaos Solitons & Fractals, 2007

We give some new definitions of D * -metric spaces and we prove a common fixed point theorem for ... more We give some new definitions of D * -metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete D * -metric spaces. We get some improved versions of several fixed point theorems in complete D * -metric spaces.

Journal of Mathematical Analysis and Applications, 2008

In this paper, we consider strongly bounded linear operators on a finite dimensional probabilisti... more In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete.

Acta Applicandae Mathematicae, 2010

The main problem analyzed in this paper consists in showing that, under some conditions, every al... more The main problem analyzed in this paper consists in showing that, under some conditions, every almost quartic mapping from a linear space to a random normed space under the Łukasiewicz t-norm can be suitably approximated by a quartic function, which is unique.

Mathematical and Computer Modelling, 2010

In this paper, we consider the concept of a Ω-distance on a complete partially ordered G-metric s... more In this paper, we consider the concept of a Ω-distance on a complete partially ordered G-metric space and prove some fixed point theorems.

Chaos Solitons & Fractals, 2008

In this paper, we consider complete Menger probabilistic quasi-metric space and prove a common fi... more In this paper, we consider complete Menger probabilistic quasi-metric space and prove a common fixed point theorem for commuting maps in this space.

Journal of Computational and Applied Mathematics, 2009

Keywords: Domain of words Quicksort algorithms Intuitionistic fuzzy metric spaces Completeness Fi... more Keywords: Domain of words Quicksort algorithms Intuitionistic fuzzy metric spaces Completeness Fixed point theorem a b s t r a c t

Applied Mathematics and Computation, 2006

The purpose of this paper is to utilize the property (E.A.) and the common property (E.A.) to pro... more The purpose of this paper is to utilize the property (E.A.) and the common property (E.A.) to prove some existence results on common fixed point for contractive mappings in fuzzy metric spaces which include fuzzy metric spaces of two types, namely, Kramosil and Michalek fuzzy metric spaces along with George and Veeramani fuzzy metric spaces. Our results generalize and extend several relevant common fixed point theorems from the literature. We also furnish an illustrative example.

Chaos Solitons & Fractals, 2008

Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073-9] proved some fixe... more Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073-9] proved some fixed point theorems in intuitionistic fuzzy metric spaces by a strong definition of Cauchy sequence (see [George and Veeramani, Fuzzy Sets Syst 1994;64:395-9] and [Veeramani and Vasuki, Fuzzy Sets Syst 2003;135:409-13]), also the intuitionistic fuzzy metric space has extra conditions (see [Gregori et al., Chaos, Solitons & Fractals, 2006;28:902-5]). In this paper, we consider generalized intuitionistic fuzzy metric spaces i.e., L-fuzzy metric spaces and prove the fuzzy version of Banach and Edelstein contraction theorems in these spaces for modified definition of Cauchy sequence.

Chaos Solitons & Fractals, 2008

Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Ve... more Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new.

Computers & Mathematics With Applications, 2010

Lee et al. considered the following quadratic functional equation f(lx+y)+f(lx−y)=2l2f(x)+2f(y) a... more Lee et al. considered the following quadratic functional equation f(lx+y)+f(lx−y)=2l2f(x)+2f(y) and proved the Hyers–Ulam–Rassias stability of the above functional equation in classical Banach spaces.In this paper, we prove the Hyers–Ulam–Rassias stability of the above quadratic functional equation in non-Archimedean L-fuzzy normed spaces.

Applied Mathematics Letters, 2010

In this work, we prove the generalized Hyers-Ulam stability of the following functional inequality: