# Madjid Eshaghi GordjiSemnan University · Faculty of Mathematics, Statistics and Computer Science

Madjid Eshaghi Gordji

Professor of Mathematics

## About

417

Publications

50,786

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5,002

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Citations since 2017

Introduction

I work in Game Theory and cognitive sciences.

Additional affiliations

August 2003 - July 2016

August 2003 - present

## Publications

Publications (417)

In this paper, authors offer one novel mathematical model of credit lending to customers based on evolutionary game theory, and the model presents an efficient and realistic approach. The purpose of the article is to examine the evolutionary game between banks and customers for granting facilities and credit. Authors assumed that customers are divi...

Artificial intelligence is the knowledge of knowing and designing intelligent agents, although the topic of artificial intelligence is very attractive, its challenges are equally important. The dangers of a robot's wrong decisions in confronting humans or two robots and other problems of wrong decisions by robots have been the concern of many scien...

In the present paper, by using orthogonally fixed point methods we prove the stability and hyperstability of orthogonally Pexider Lie homomorphisms and derivations on orthogonally Lie Banach algebras.

In this paper, we introduce a weak form of amenability on topological semigroups that we call \(\varphi \)-amenability, where \(\varphi \) is a character on a topological semigroup. Some basic properties of this new notion are obtained and by giving some examples, we show that this definition is weaker than the amenability of semigroups. As a notic...

Using fixed point methods, we prove the stability of orthogonally ring homomorphism and orthogonally ring derivation in Banach algebras.

Prediction of groundwater level (GWL) is an important issue for optimal planning and management of groundwater resources. MODFLOW, which is a modular, 3D, finite-difference model, is widely used to simulate GWL. Although MODFLOW is a powerful model for estimating GWLs, it has some unknown parameters, such as specific yield (Sy) and hydraulic conduc...

This work aims to provide insights on how decision making in a healthcare setting can be guided by game theory. We believe that our research letter makes a significant contribution to the literature because it can equip surgeons in the health-care system with the necessary strategies to make efficient decisions by introducing them to game theory, w...

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction. Likewise, the brain networks’ complexity arises from interactions beyond pair connections, as it is simplistic to assume that in complex networks state of a link is independently determin...

In this paper, we introduce the concept of $C^*$-ternary $3$-Jordan derivation on the $C^*$-ternary algebras. Then we prove that the $3$-linearity and Ulam-Hyers stability of the functional equation
$$ f(x_{1} + x_{2}, y_{1} + y_{2}, z_{1} + z_{2})= \sum_{1\leq i,j,k\leq2} f(x_{i}, y_{j} , z_{k})$$
in $C^*$-ternary algebras.

Purpose: This article aims to study trade tensions between advanced economies and to express the difference between "currency war" and "trade war" and the respective effects on the global economy.
Design/Methodology/Approach: The analysis of trade relations between countries is always one of the main concerns of policymakers and economists. In thi...

In this article, we study the impact of teamwork on an organization's performance, considering a cooperative game's framework. To promote teamwork culture, performance indexes were considered both individually and collectively, and by comparing the scores that every employee earned individually and collectively, their differences became obvious. In...

What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction. Likewise, the brain networks' complexity arises from interactions beyond pair connections, as it is simplistic to assume that in complex networks state of a link is independently determin...

In this paper, a new and applied concept of topological spaces based upon relations is introduced.
These topological spaces are called R-topological spaces and SR-topological spaces. Some of the properties of these spaces and their relationship with the initial topological space are verified. Moreover, some of their applications for example in fixe...

In this paper, we provide an interpretation of the rationality in game theory in which players consider the profit or loss of the opponent in addition to personal profit at the game. The goal of a game analysis with two hyper-rationality players is to provide insight into real-world situations that are often more complex than a game with two ration...

In this paper, we introduce a weak form of amenability on topological semigroups that we call $\varphi$-amenability, where $\varphi$ is a character on a topological semigroup. Some basic properties of this new notion are obtained and by giving some examples, we show that this definition is weaker than the amenability of semigroups. As a noticeable...

The purpose of this paper is to introduce the notion of R-metric spaces and give a real generalization of Banach fixed point theorem. Also, we give some conditions to construct the Brouwer fixed point. As an application, we find the existence of solution for a fractional integral equation.

In this paper, we consider the stability and nonstability results for the following system of functional equations
where a, b ∈ ℤ\{0}, on r-divisible abelian groups.

The aim of this paper is to model North Korea and USA relationship since past until now. To this end, we have used game theory. The weakness of the existing models is that they have a static nature and can't analyze the changes of processes, strategies and results. The dynamic system of strategic games of which we have used in this article is a pro...

Water resources scarcity and competition among stakeholders in water allocation always highlights the optimal operation of water resources. This research examines the operation of a multi-purpose water reservoir aiming at providing agricultural, urban, industrial and environmental demands. A new evolutionary Hybrid Algorithm (integrating Bat Algori...

The rational choice theory is based on this idea that people rationally pursue goals for increasing their personal interests. Here, we present a new concept of rational choice as a hyper-rational choice in which the actor thinks about profit or loss of other actors in addition to his personal profit or loss and then will choose an action that is de...

The problems of budgeting in Iran are more than one of the government policies, because of traditional processes in preparation, adoption and implementation of budgets. The purpose of this paper is to provide a model for the distribution and optimization of credit allocation of provincial capital assets between the provinces. For this purpose, game...

In this study, considering the importance of how to exploit renewable natural resources, we analyze a fishing model with nonlinear harvesting function in which the players at the equilibrium point do a static game with complete information that, according to the calculations, will cause a waste of energy for both players and so the selection of coo...

In this paper, among the other things, we show that the solution of the first-orderdifferential equation is a fixed point of an integral operator from an orthogonal metric space into itself. This approach provides a new proof of the classical existence and uniqueness theorems of solutions to a first-order differential equation.

In this paper, a new interpretation of the rationality for modeling in the game theory has been proposed. The advantage of this concept emphasizes the importance of outcomes of other actors in game. The hyper-rationality concept focuses on preferences of actors how seek to
maximize benefit or loss of other actors and or seek to maximize his benefit...

In this paper, we present a model of Partnership Game with respect to the important role of partnership and cooperation in nowdays life. Since such interactions are repeated frequently, we study this model as a Stage Game in the structure of infinitely repeated games with a discount factor $\delta$ and Trigger strategy. We calculate and compare the...

Analysis of political and economic relations between the two countries has always been one of the concerns of elites and analysts of both countries as well as third countries. Game theory is a powerful tool for analyzing international relations and achieving the desired goals. In this article, by using dynamic system of strategic games, which is a...

In this article, we show that how human decision makers behave in interactive decisions. We interpret the players’ behavior with help of the concept of hyper-rationality. These interpretations help to enlarge our understanding of the psychological aspects of strategy choices in games. With help of this concept can be analyzed social sciences and so...

In this paper, with help of the concept of hyper-rationality, we model the interaction between two investment companies by an important game as trickery game that has special equilibrium which called hyper-equilibrium. In trickery game, one company can choose cooperation with another company until the last moment and finally changes his action to n...

The acknowledgment in the original article is incomplete.

By studying game theory, we find that the Nash equilibrium does not exist in some games or, if there is in one, does not describe a real event. Here we show that the matching pennies game with pure strategy has the solution, but this solution is a game that happens simultaneously with this game. Using this solution, we will answer the Brookings Ins...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-
type stability of the conditional of orthogonally ring $* $-$ n $-derivation and orthogonally
ring $* $-$ n $-homomorphism on $ C^* $-algebras. As a consequence of this, we prove the
hyperstability of orthogonally ring $* $-$ n $-derivation and orthogonally...

We study the concept of parallel sum of positive adjointable operators on a Hilbert \(C^*\)-module and present several characterizations for that. Moreover we show that the set of all positive adjointable operators has semilattice structure with this operation. Finally the infimum of two orthogonal projection over a Hilbert \(C^*\)-module is charac...

Recently Eshaghi et al. introduced orthogonal sets and proved the real generalization of the Banach fixed point theorem on these sets. In this paper, we prove the real generalization of Diaz–Margolis fixed point theorem on orthogonal sets. By using this fixed point theorem, we study the stability of orthogonally \(*\)-m-homomorphisms on Lie \(C^*\)...

In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form.

In this paper, we are interested in obtaining fixed point theorems by keeping the orthogonal completeness of the orthogonal metric space and replacing the (Formula presented.)-contraction condition in theorems by another slightly modified conditions. The paper contains an example illustrating our results.

Understanding of the atomic structures and ways in which the atoms interacting is critical to the understanding of chemistry. In this paper applied the concepts of game theory in explaining reactions between elements of the periodic table. The findings in this study suggest that the coordination and anti coordination, also cooperation and non-coope...

This work explores dynamics existing in interactions between players. The dynamic system of games is a new attitude to modeling in which an event is modeled using several games. The model allows us to analyze the interplay capabilities and the feasibility objectives of each player after a conflict with other players objectives and capabilities. As...

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then C(⊆ X) is functionally convex (briefly, F-convex), if T (C) ⊆ R is convex for all bounded linear transformations T ∈ B(X, R); and K(⊆ X) is functionally closed (briefly, F-closed), if T (K) ⊆ R is closed for all bounded linear t...

Maybe an event can't be modeled completely through on game but there is more chance with several games. With emphasis on players' rationality, we present new properties of strategic games, which result in production of other games. Here, a new attitude to modeling will be presented in game theory as dynamic system of strategic games and its some ap...

In this article, we introduce a kind of binary relation on a nonempty set with name of orthogonally relation which we develop for sequences, continuous maps, metric spaces, contraction maps, preserving maps and etc. All of the above concepts are generalized forms of ordinary case, so they are very important for extension and finding new results. we...

The classical Jensen inequality for concave function \(\varphi \) is adapted for the Sugeno integral using the notion of the subdifferential. Some examples in the framework of the Lebesgue measure to illustrate the results are presented.

Hermite-Hadamard inequality is an important integral inequality in mathematics giving upper and lower bounds for the integral average of convex (concave) functions defined on closed intervals. Sandor's inequality is the same Hermite-Hadamard inequality but for the square of convex (concave) functions. In this paper, Sandor's inequality for nonlinea...

We introduce the notion of the orthogonal sets and give a real generalization of Banach’ fixed point theorem. As an application, we find the existence of solution for a first-order ordinary differential equation. © 2017, Springer International Publishing. All rights reserved.

In this paper, we introduce the concept of a logarithmic convex structure. Let $X$ be a set and $D\colon X\times X\rightarrow[1,\infty)$ a function satisfying the following conditions: \item{(i)} For all $x,y\in X$, $ D(x,y)\geq1$ and $D(x,y)=1$ if and only if $x=y$. \item{(ii)} For all $x,y\in X$, $D(x,y)=D(y,x)$. \item{(iii)} For all $ x,y,z\in X...

In this paper, we investigate the Ulam-Hyers stability of C*-ternary 3-Jordan homomorphisms for the functional equation f(x(1) + x(2), y(1) + y(2), z(1) + z(2)) = Sigma(1 <= i,j,k <= 2) f(x(i),y(j),z(k)) in C*-ternary algebras.

Let A and B be real ternary Banach algebras. An additive mappings : (A, [ ](A)) -> (B, [ ](B)) is called a ternary Jordan homomorphism if ([x, x, x](A)) = [(x), (x)](B) for all x is an element of A. In this paper, we investigate the stability and superstability of ternary Jordan ring homomorphisms in ternary Banach algebras by using the fixed point...

Shokri et al. [Approximate bihomomorphisms and biderivations in 3-Lie algebras, Int. J. Geom. Methods Mod. Phys. 10 (2013) 1220020, 13pp.] proved the Hyers–Ulam stability of bihomomorphisms and biderivations on normed 3-Lie algebras. It is easy to see that the definition of bihomomorphism in normed 3-Lie algebras is meaningless and so the results o...

We prove the Hyers-Ulam stability of ternary Jordan bi-derivations on Banach Lie triple systems associated to the Cauchy functional equation.

The rational choice theory is based on this idea that people rationally pursue goals for increasing their personal interests. In most conditions, the behavior of an actor is not independent of the person and others' behavior. Here, we present a new concept of rational choice as hyper-rational choice which in this concept, the actor thinks about pro...

Beginning around 1980, the topic of approximate homomorphisms, or the stability of the equation of homomorphism, was taken up by a number of mathematicians. Some of these studies are presented in the book of Hyers et al., among others. In this chapter, approximate homomorphisms and derivations in ordinary Banach algebras are studied. Then, homomorp...

After defining the functional equations of various degrees, it was predictable to define the different mixtures of those functional equations. So, binary mixtures, ternary mixtures and foursome mixtures of functional equations were defined. In this chapter, various kinds of binary mixtures of functional equations are studied. Then, the functional e...

The functional equation f(x + y) = f(x) + f(y) was solved by A.L. Cauchy in 1821. In honor of A.L. Cauchy, it is often called the Cauchy functional equation. The properties of the Cauchy equation are powerful tools in almost every field of natural and social sciences. In this chapter, the theorem of Hyers and the so-called “direct method” is invest...

In this chapter, a new system of functional equations known as the orthogonal Pexider derivation is introduced. The stability and hyperstability of this class of functional equations, including the orthogonal Pexider ring derivation and the orthogonal Pexider Jordan ring derivation, are investigated by using the fixed point method. Consequently, so...

All the literature on the stability of functional equations focuses on the case where the relevant domain is an Abelian group or a normed space. In this chapter, the stability of functional equations on amenable groups is investigated. Consequently, some open problems will be stated.

We prove the Hyers-Ulam stability of ternary Jordan bi-homomorphism in Banach Lie triple systems associated to the Cauchy functional equation.

Let A be a Banach ternary algebra. An additive mapping D : (A,[]) -> (A,[]) is called a ternary Jordan ring derivation if D([xxx]) = [D(x)xx] + [xD(x)x] + [xxD(x)] for all x is an element of A. In this paper, we prove the Hyers-Ulam stability of ternary Jordan ring derivations on Banach ternary algebras.

In this paper, we use a fixed point method to prove the stability of ternary m-derivations on ternary Banach algebras.

In this paper, we define an intuitionistic fuzzy 2-normed space. Using the fixed point alternative approach, we investigate the Hyers-Ulam stability of the following quadratic functional equation f(ax + by) + f(ax - by) = a/2 f (x + y) + a/2 f(x - y) + (2a(2) - a)f (x) + (2b(2) - a) f (y) in intuitionistic fuzzy 2-Banach spaces.

In this paper, the classical Jensen inequalities for concave function φ, i.e., φ(∫f(x)dμ)⩾∫φ(f)dμandφ(∑i=1nλixi)⩾∑i=1nλiφ(xi),
are adapted for the Sugeno integral using the notion of the supergradient. Moreover, we give some modifications of previous results of Román-Flores et al. concerning Jensen-type inequalities for Sugeno integral. Some exampl...

Using the fixed point method, we prove the stability and the hyperstability of generalized orthogonally quadratic ternary homomorphisms in non-Archimedean ternary Banach algebras.

In this paper, we prove some fixed point theorem on orthogonal spaces. Our result improve the main result of the paper by Eshaghi Gordji et al. [On orthogonal sets and Banach fixed point theorem, to appear in Fixed Point Theory]. Also we prove a statement which is equivalent to the axiom of choice. In the last section, as an application, we conside...

Ebadian et al. proved the Hyers-Ulam stability of bimultipliers and Jordan bimultipliers in C*-ternary algebras by using the fixed point method. Under the conditions in the main theorems for bimultipliers, we can show that the related mappings must be zero. Moreover, there are some mathematical errors in the statements and the proofs of the results...

In this paper, we introduce functional equations in G-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete G-normed spaces by using the fixed point method.

In this paper, it is shown that the Hadamard integral inequality for r-convex functions is not satisfied in the fuzzy context. Using the classical Hadamard integral inequality, we give an upper bound for the Sugeno integral of r-convex functions. In addition, we generalize the results related to the Hadamard integral inequality for Sugeno integral...

Let X be a vector space over a field K of real or complex numbers and k ∈ ℕ. We prove the superstability of the following generalized Golab–Schinzel type equation (equation found), where f: X → K is an unknown function which is hemicontinuous at the origin.

Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stabilit...

In this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable
f(∑i=1paixi)=∑i=1paif(xi)$f\left(\sum\nolimits_{i = 1}^p {a_i x_i } \right) = \sum\nolimits_{i = 1}^p {a_i f(x_i )}$
in an intuitionistic fuzzy Banach space. Then, we conclude the results for Cauchy–Jensen functional equa...

Let X be a real normed space, then C(⊆ X) is functionally convex (briefly, F-convex), if T (C) ⊆ R is convex for all bounded linear transformations T ∈ B(X, R); and K(⊆ X) is functionally closed (briefly, F-closed), if T (K) ⊆ R is closed for all bounded linear transformations T ∈ B(X, R). We improve the Krein-Milman theorem on finite dimensional s...

The purpose of this paper is to present some Pata type fixed point theorems
for multivalued mappings on ordered complete metric spaces. Moreover, as
an application of our main theorem, we give an existence theorem for the solution
of a hyperbolic differential inclusion problem

In this paper, we prove that (θ,ϕ)*-derivations on complex semi–prime *-algebras can be represented by double (θ,ϕ)*-centralizers. As an application, we prove a result in automatic continuity of (θ,ϕ)*-derivations and α-derivations.

Let Xρ be a ρ-complete modular space. A mapping f : Xρ → Xρ is called an ε-isometry if |ρ (f(x) - f(y)) - ρ(x - y) | ≤ ε for all x, y ∈ Xρ. By making use of a direct method, it is shown that there exists an isometry I : Xρ → Xρ and constants A, B such that if f : Xρ → Xρ is an ε-isometry, then ρ(f(x) - I(x)) ≤ Aρ(x) + Bε, where I(x) is ρ-limit sequ...

In the present paper, we introduce a new system of functional equations, known as orthogonal Pexider derivations. We investigate the stability and hyperstability of this class of functional equations, including the orthogonal Pexider ring derivation and the orthogonal Pexider Jordan ring derivation, by using the fixed point method.

In this paper, we introduce the concept of generalized contraction for multivalued operators defined on ordered complete metric spaces. We analyze the existence of fixed points for generalized multivalued operators. Moreover, as an application of our main theorem, we give an existence theorem for the solution of a hyperbolic differential inclusion...

In this paper, we introduce the concept of normed Lie superalgebras and define the superhomomorphism and the superderivation in normed Lie superalgebras. We define a generalized T-orbitally complete metric space and prove a new fixed point alternative concerning the stability problem of functional equations. Consequently, we deal with the stability...

In [1], the definition of C*-Lie ternary (?,?,?)-derivation is not well-defined and so the results of [1, Section 4] on C*-Lie ternary (?,?,?)-derivations should be corrected.

In this paper, we give an upper bound for the Sugeno fuzzy integral of log-convex functions using the classical Hadamard integral inequality. We present a geometric interpretation and some examples in the framework of the Lebesgue measure to illustrate the results.

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.