Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(H). Manuscript profile

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 non-cooperation which incur more loss to an opponent. Indeed, the hyper-equilibrium is the point in which only one player can displace equilibrium to another point by changing his action which causes profit or loss to other players so they cannot change their action. Our findings indicate that the kind of behaviour interactive, environmental conditions, and valuation system are based on hostility causes an equilibrium point to incur the maximum loss to an opponent. Manuscript profile

In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation. Manuscript profile

In this paper, we first present the new concept of $2$-normed algebra.We investigate the structure of this algebra and give some examples.Then we apply a fixed point theorem to prove the stability and hyperstability of $(\alpha, \beta, \gamma)$-derivations in $2$-Banach algebras. Manuscript profile

‎In this paper‎, ‎first we introduce the notion of $\frac{1}{2}$-modular metric spaces and weak $(\alpha,\Theta)$-$\omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an example to illustrate the usability of these theorems‎. Manuscript profile