# Ismail NikoufarPayame Noor University | PNU · Department of Mathematics

Associate Professor in Mathematics

49
Publications
1,894
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
329
Citations
December 2005 - present
Position
• Professor (Assistant)

## Publications

Publications (49)
Preprint
Full-text available
In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type inequality and a multiple operator version of the Jensen's inequality for $h$-convex functions. In particular...
Preprint
Full-text available
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's inequality, arithmetic-geometric mean inequality, Chrystal inequality, and H\"older-McCarthy inequality. Many o...
Preprint
Full-text available
In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for $s$-convex function. We also give an application to the order preserving power inequality of three variables and find a better lower bound for the numerical radius of a positive operator under some conditions.
Article
Let fi, i 2 {1, 2, . . . ,k}, be an analytic function on the unit disk in the complex plane of the form fi(z) = zn + ai,n+1zn+1 + . . . , n 𝜖 ℕ = {1, 2, . . .}. We consider the following Frasin integral operator:Gnz=∫0znξn−1f1′ξnξn−1α1⋯fk′ξnξn−1αkdξ. We establish a sufficient condition under which this integral operator is n-valent convex and obtai...
Article
Full-text available
The objective of this paper is to reveal an operator version of the Jensen inequality and its reverse one for s-convex functions and self-adjoint operators on a Hilbert space. We improve the Hölder–McCarthy inequality by providing an upper bound. Some particular cases and applications will be also considered.
Article
Wigner and Yanase conjectured the more general problem of the concavity of the function $$\rho \mapsto \text {Trace}\ \rho ^pK^*\rho ^{1-p}K$$. Lieb gave an actual connection with something then known as the strong subadditivity of the quantum entropy conjecture, which was due to Ruelle and Robinson. Lieb proved the concavity of that function, and...
Article
In this paper, we give a new characterization for the perspective of a continuous function under certain assumptions. This result generalizes a non-commutative analogue of the arithmetic–geometric mean inequality. Our main result extends and strengthens the existing result concerning the characterization of the geometric operator mean. We provide t...
Article
Full-text available
The relative operator entropy has properties like operator means. In addition, the relative operator entropy has entropy-like properties. In this paper, we prove a Loewner–Heinz type inequality for operator monotone and multiplicative-additive functions and its converse and apply it to the relative operator entropy. We identify the equivalence rela...
Article
Full-text available
In this paper, we investigate the lower and upper bound of the relative operator (α,β)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha ,\beta )$$\end{document}-e...
Preprint
In this paper, we provide some inequalities for $P$-class functions and self-adjoint operators on a Hilbert space including an operator version of the Jensen's inequality and the Hermite-Hadamard's type inequality. We improve the H\"{o}lder-MacCarthy inequality by providing an upper bound. Some refinements of the Jensen type inequality for $P$-clas...
Article
Full-text available
In this paper, we present some inequalities for the generalized relative operator entropy according to the generalized Tsallis relative operator entropy. Our results are generalizations of some existing inequalities.
Article
Full-text available
In this paper, we provide some inequalities for P-class functions and self-adjoint operators on a Hilbert space including an operator version of the Jensen?s inequality and the Hermite-Hadamard?s type inequality. We improve the H?lder-MacCarthy inequality by providing an upper bound. Some refinements of the Jensen type inequality for P-class functi...
Article
We introduce the notion of the generalized type derivation and identify its decompositions. We obtain some results concerning continuity of generalized type derivations on $$C^*$$-algebras. Our results recover continuity of ordinary derivations, right (left) centralizers and double derivations on $$C^*$$-algebras.
Article
In this paper, we establish behavior of almost bi-cubic functions in Lipschitz spaces. Indeed, we give a set-valued and Lipschitz norm approximation of bi-cubic functional equations in Lipschitz spaces.
Article
In this paper, we introduce the notion of multivariate generalized perspectives and verify the necessary and sufficient conditions for operator convexity (resp. concavity) of this notion. We also establish the crossing of the multivariate generalized perspective of regular operator mappings under completely positive linear maps and partial traces.
Article
The Loewner–Heinz inequality is not only the most essential one in operator theory, but also a fundamental tool for treating operator inequalities. The aim of this paper is to investigate the converse of the Loewner–Heinz inequality in the view point of perspective and generalized perspective of operator monotone and multiplicative functions. Indee...
Article
The algebra of Lipschitz functions on a complete metric space plays a role in non-commutative metric theory similar to that played by the algebra of continuous functions on a compact space in non-commutative topology. The notion of stability of functional equations was posed by Ulam, and then, Hyers gave the first significant partial solution in 19...
Article
Full-text available
In this paper, we determine the bounds of the generalized relative operator entropy in general. In particular, we identify the bounds of the parametric extension of the Shannon entropy and of the generalized Tsallis relative operator entropy. Moreover, we improve the upper bound of the relative operator entropy in some sense.
Article
Full-text available
In this paper, we identify upper and lower bounds of the generalized relative operator entropy based on the notion of perspectives. Moreover, we find upper and lower bounds of the Tsallis relative operator entropy to specify the bounds of the relative operator entropy.
Article
Full-text available
In this paper, we introduce two notions of a relative operator ( α , β )-entropy and a Tsallis relative operator ( α , β )-entropy as two parameter extensions of the relative operator entropy and the Tsallis relative operator entropy. We apply a perspective approach to prove the joint convexity or concavity of these new notions, under certain condi...
Article
Full-text available
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed valu...
Article
Full-text available
In this paper, we consider Lipschitz conditions for tri-quadratic functional equations. We introduce a new notion similar to that of the left invariant mean and prove that a family of functions with this property can be approximated by tri-quadratic functions via a Lipschitz norm.
Article
Full-text available
Lieb’s extension theorem holds for generalized p + q ∈ [0; 1] and Ando convexity theorem holds for q - r > 1. In this paper, we give a complete characterization for concavity or convexity of Lieb well known theorem in the case where p + q ≥ 1 or p+q ≤ 0. We also characterize some auxiliary results including Ando theorem for q-r ≤ 1.
Article
Full-text available
In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.
Article
In our original paper, we approximated the quartic functional equations in Lipschitz spaces. In the present paper, we demonstrate the results presented in our recent paper only hold for quadratic functional equations and then we correct our results and approximate the quartic functional equations in Lipschitz spaces.
Article
In this paper, under certain conditions we find a double Jordan derivation near a certain function in a p-Banach algebra. Indeed, we prove the generalized Hyers–Ulam–Rassias stability and Isac-Rassias stability of double Jordan derivations in p-Banach algebras.
Article
Full-text available
In this paper, we present some refinements and precise estimations of parametric extensions of Shannon inequality and its reverse one given by Furuta in Hilbert space operators. We also demonstrate an extension of operator Shannon type inequality.
Article
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.
Article
In this paper, we introduce the notion of Jordan -derivations on Hilbert C*-modules and we investigate the generalized Hyers-Ulam-Rassias stability of this notion with an alternative fixed point and direct method. Moreover, we provide Hyers-Ulam, Aoki-Rassias, and Isac-Rassias type stability and superstability of Jordan -derivations and Jordan deri...
Article
In this paper we approximate the quartic functional equations in Lipschitz spaces.
Article
Let X and Y be normed spaces over a complete field F with dual spaces X' and Y' respectively. Under certain hypotheses, for given x ε X, y ε Y and a mapping u from X' × Y' to F, we apply Hyers-Ulam approach to find a unique bounded bilinear mapping ν near to u such that ||ν|| = ||x ⊗ y||.
Article
Full-text available
In this paper, our approach allows to refine the results announced by Ebadian et al. [Results Math., 36 (2013), 409-423]. Namely, we reduce the distance between approximate and exact double derivations on Banach algebras and Lie C*-algebras up to 1/2n-1 and 1/2n-2 for n ≥ 2. Indeed, we give a correct utilization of fixed point theory in the sense o...
Article
In this short note we give a novel proof to show that for an infinite-dimensional Hilbert space, a basis is never a Hamel basis.
Article
In our recent paper, we introduced the notions of relative operator (α,β)(α,β)-entropy and Tsallis relative operator (α,β)(α,β)-entropy as a parameter extensions of relative operator entropy and Tsallis relative operator entropy. In this paper, we give upper and lower bounds of these new notions according to operator (α,β)(α,β)-geometric mean intro...
Article
We generalize the celebrated theorem of Johnson and prove that every left θ -centralizer on a semisimple Banach algebra with left approximate identity is continuous. We also investigate the generalized Hyers–Ulam–Rassias stability and the superstability of θ -centralizers on semiprime Banach *-algebras.
Article
In page 1975 of [W. Roth, A uniform boundedness theorem for locally convex cones, Proc. Amer. Math. Soc. 126 (1998), no.7, 1973-1982] we can see: In a locally convex vector space E a barrel is defined to be an absolutely convex closed and absorbing subset A of E. The set U={(a,b)∈E2, a−b∈A} then is seen to be a barrel in the sense of Roth's definit...
Article
In this paper, by applying jointly concavity and jointly convexity of generalized perspective of some elementary functions, we give the simplest proof of the well-known Lieb concavity theorem and Ando convexity theorem.
Article
In this paper, we investigate generalized Jordan derivations on Frechet algebras. Moreover, we prove the generalized Hyers-Ulam-Rassias stability and superstability of generalized Jordan derivations on Frechet algebras. An important issue is so that we do not assume that the Frechet algebra is unital.
Article
In this paper, we introduce the notion of (θ 1 ,θ 2 ,θ 3 ,ϕ)-derivations on Hilbert C * -modules. Moreover, we investigate the generalized Hyers-Ulam-Rassias stability, Isac-Rassias type stability and superstability of (θ 1 ,θ 2 ,θ 3 ,ϕ)-derivations on Hilbert C * -modules.
Article
In this article, we introduce the notion of generalized derivations on Hilbert C*-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equation rf x + y r + sg x − y s = 2h(x) for r, s ∈ R \ {0} on Hilbert C*-modules, where f, g, and h are mappings fro...
Article
Full-text available
In this paper, we generalize the main results of [Effros EG, (2009) Proc Natl Acad. Sci USA 106:1006-1008]. Namely, we provide the necessary and sufficient conditions for jointly convexity of perspective functions and generalized perspective functions.

Cited By