Rahmatollah Lashkaripour

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• Professor
• Professor (Full) at University of Sistan and Baluchestan

This paper presents several numerical radius and norm inequalities for Hilbert space operators.

In this paper, we present several improvements and extensions to inequalities related to the numerical radius of operators in terms of the angle between two vectors in Hilbert space.

Let B(H) denote the set of all bounded linear operators on a complex Hilbert space H. In this paper, the authors present some norm inequalities for sum of operators which are a generalization of some recent results. Among other inequalities, it is shown that if S, T ∈ B(H) are normal operators, then ∥S + T∥ ≤ 1 2 (∥S∥ + ∥T∥) + 1 2 √ (∥S∥ − ∥T∥) 2 +...

In this paper, the structured distance in the Frobenius norm of a real irreducible tridiagonal 2-Toeplitz matrix T to normality is determined. In the first part of the paper, we introduced the normal form a real tridiagonal 2-Toeplitz matrix. The eigenvalues of a real tridiagonal 2-Toeplitz matrix are known. In the second part of this paper, we dis...

In this article, we explore further properties of the generalized numerical radius. More precisely, we show several inequalities for the generalized numerical radius wN(·), with some emphasize on p-Schatten numerical radius wp(·)(p≥1) of Hilbert space operators.

Let ${\mathbb B}(\mathscr H)$ denote the set of all bounded linear operators on a complex Hilbert space ${\mathscr H}$. In this paper, we present some norm inequalities for sums of operators which are a generalization of some recent results. Among other inequalities, it is shown that if $S, T\in {\mathbb B}({\mathscr H})$ are normal operators, then...

In this article, the concept of the A-Davis-Wielandt Berezin number is introduced for positive operatorA. Some upper and lower bounds for the A-Davis-Wielandt Berezin number are proved. Moreover, some inequalities related to the concept of the Davis-Wielandt Berezin number are obtained, which are generalizations of known results. Among them, it is...

In this paper, we study the multiple solutions of parametric quasilinear systems of the gradient-type on the Sierpi´nski gasket arising in physical problems leading to nonlinear models involving reaction-diffusion equations, in problems on elastic fractal media or fluid flow through fractal regions. By using some critical point theorems, we give so...

In this paper, we present several Berezin number inequalities involving extensions of Euclidean Berezin number for n operators. Among other inequalities for (T1,..., Tn) ? B(H) we show that berp p(T1,..., Tn) ? 1 2p ber (?n i=1 (|Ti| + |T* i|)p), where p > 1.

In this paper, we establish some upper bounds for Berezin number inequalities including of $2\times 2$ operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if $T=\left[\begin{array}{cc} 0&X\\ Y&0 \end{array}\right]$, then \begin{align*} \textbf{ber}^{r}(T)\leq 2^{r-2}\left(\textbf{ber}(f^{2r}(|X|)+g^{2r}(|Y^*|)...

In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of Olgun, Minak and Altun [M. Olgun, G. Minak and I. Altun, A new approach to Mizoguchi–Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 2016, 3, 579–587], we improve these theorems with...

In this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders $\gamma \in \left({n}_{1}-1,{n}_{1}\right]$ and $\eta \in \left({n}_{2}-1,{n}_{2}\right]$ for any ${n}_{1},{n}_{2}\in \mathrm{ℕ}$ . We deals with existence and uniqueness of solutions for the problem. The approach is based on the K...

Abstract In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improvement for Fazli–Nieto’s results with some conditions removed based on a new technique is the main objective of this paper. In add...

Abstract In this paper, we present some unitarily invariant norm inequalities for sector matrices involving a special class of functions. In particular, if Z = ( Z 11 Z 12 Z 21 Z 22 ) is a 2 n × 2 n $2n\times 2n$ matrix such that numerical range of Z is contained in a sector region S α $S_{\alpha } $ for some α ∈ [ 0 , π 2 ) $\alpha \in [0,\frac{\p...

In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space $\mathcal H=\mathcal H(\Omega)$ and also improve them. Among other inequalities, it is shown that if $A,B\in {\mathcal B}(\mat...

In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequality. In particular, we present w_{p}^{p}(A_{1}^{*}T_{1}B_{1},\dots,A_{n}^{*}T_{n}B_{n})\leq\frac{n^{1-\frac{1% }{r}}}{2^{\frac{1}{r}}}\bigg{\|}\sum_{i=1}^{n}[B_{i}^{*}f^{2}(|T_{i}|)B_{i}]^{% rp}+[A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i}...

We present some inequalities related to the Hilbert-Schmidt numerical radius of 2 x 2 operator matrices. More precisely, we present a formula for the Hilbert-Schmidt numerical radius of an operator as follows: w2(T) = sup ?2+?2=1 ||?A + ?B||2, where T = A + iB is the Cartesian decomposition of T ? HS(H).

In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a Hilbert space and also improve them. Among other inequalities, it is shown that if $A,B\in {\mathcal B}(\mathcal H)$ such that $|A|B=B^{*}|A|$, $f$ and $g$ are...

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessar...

In this paper, we introduce the new notion of generalized proximal α-h-φ-contraction mappings and investigate the existence of the best proximity point for such mappings in the complete metric spaces.

In this article, by introducing a new operator, we give a new generalization contraction condition for multi valued maps. Moreover, without assumption of lower semi continuity, we prove some fixed point theorems in incomplete metric spaces. Our results are extension of the corresponding results of I. Altun et al.(Nonlinear Analysis: Modeling and co...

In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of M. Olgun et al.(J. Nonlinear Convex Anal., 17(3), 2016, 579-587), we give a new generalization contraction condition for multivalued mappings and prove some fixed point theorems in incomplete metric s...

In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of M. Olgun et al.(J. Nonlinear Convex Anal., 17(3), 2016, 579-587), we give a new generalization contraction condition for multivalued mappings and prove some fixed point theorems in incomplete metric s...

Abstract In this paper, we introduce the concept of comparable complete metric spaces and consider some fixed point theorems for mappings in the setting of incomplete metric spaces. We obtain the results of Ansari et al. [J. Fixed Point Theory Appl. 20:26, 2018] with weaker conditions. Moreover, we provide some corollaries and examples show that ou...

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessar...

In this paper, we give some reverse-types of Ando’s and Hölder–McCarthy’s inequalities for positive linear maps, and positive invertible operators. For this purpose, we use a recently improved Young inequality and its reverse.

We generalize several inequalities involving powers of the numerical radius for off-diagonal part of $2\times2$ operator matrices of the form $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, where $B, C$ are two operators. In particular, if $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, then we get \begin{align*} {1\over 2^{{3\ove...

In this paper, we give some reverse-types of Ando's and H\"older-McCarthy's inequalities for positive linear maps, and positive invertible operators. For our purpose, we use a recently improved Young inequality and its reverse.

In this paper, we give some reverse-types of Ando's and H\"{o}lder-McCarthy's inequalities for positive linear maps, and positive invertible operators. For our purpose, we use a recently improved Young inequality and its reverse.

In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequalities. In particular, we present \begin{align*} w_{p}^{p}(A_{1}^{*}T_{1}B_{1},...,A_{n}^{*}T_{n}B_{n})\leq\frac{n^{1-\frac{1}{r}}}{2^{\frac{1}{r}}}\Big\|\sum_{i=1}^{n}[B_{i}^{*} f^{2}(|T_{i}|)B_{i}]^{rp}+[A_{i}^{*}g^{2}(|T_{i}^{...

In this paper, we generalize several Berezin number inequalities involving product of operators. For instance, we show that if $A, B$ are positive operators and $X$ is any operator, then \begin{align*} \textbf{ber}^{r}(H_{\alpha}(A,B))&\leq\frac{\|X\|^{r}}{2}\textbf{ber}(A^{r}+B^{r})&\leq\frac{\|X\|^{r}}{2}\textbf{ber}(\alpha A^{r}+(1-\alpha)B^{r})...

In this paper, we generalize several Berezin number inequalities involving product of operators, which acting on a Hilbert space . Among other inequalities, it is shown that if A,B are positive operators and X is any operator, then where , , , and .

In this paper, we generalize some matrix inequalities involving matrix power and Karcher means of positive definite matrices. Among other inequalities, it is shown that if ${\mathbb A}=(A_{1},...,A_{n})$ is a $n$-tuple of positive definite matrices such that $0<m\leq A_{i}\leq M\, (i=1,\cdots,n)$ for some scalars $m< M$ and $\omega=(w_{1},\cdots,w_...

In this paper, a system of generalized operator equilibrium problems(for short, SGOEP) in the setting of topological vector spaces is introduced. Applying some properties of the nonlinear scalarization mapping and the maximal element lemma an existence theorem for SGOEP is proved. Moreover, using Ky Fan’s lemma an existence result for the generaliz...

In this paper, a new form of the symmetric vector equilibrium problem is introduced and, by mixing properties of the nonlinear scalarization mapping and the maximal element lemma, an existence theorem for it is established. We show that Ky Fan’s lemma, as a usual technique for proving the existence results for equilibrium problems, implies the maxi...

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if $A, B, X$ are $n\times n$ matrices, then \begin{align*} \|AXB^*\|^2\leq\|f_1(A^*A)Xg_1(B^*B)\|\,\|f_2(A^*A)Xg_2(B^*B)\|, \end{align*} where $f_1,f_2,g_1,g_2$ are non-negative continues functions...

In this paper we introduce the concept of the best triplex common proximity point in G-metric space (X;G), as extension of the best proximity point in metric spaces. Also we provide su�cient conditions for the existence of a unique best triplex common proximity point for some mappings in complete G-metric spaces. At the end, we show that some of th...

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if $A, B, X$ are $n\times n$ matrices, then \begin{align*} \|AXB^*\|^2\leq\|f_1(A^*A)Xg_1(B^*B)\|\,\|f_2(A^*A)Xg_2(B^*B)\|, \end{align*} where $f_1,f_2,g_1,g_2$ are non-negative continues functions...

We generalize several inequalities involving powers of the numerical radius for off-diagonal part of $2\times2$ operator matrices of the form $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, where $B, C$ are two operators. In particular, if $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, then we get \begin{align*} {1\over 2^{{3\ove...

In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two positive semidefinite matrices $A$ and $B$ we show that \begin{align*} \Big\|A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}\Big...

In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two positive semidefinite matrices $A$ and $B$ we show that \begin{align*} \Big\|A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}\Big...

In this paper, we generalize some matrix inequalities involving matrix power and Karcher means of positive definite matrices. Among other inequalities, it is shown that if ${\mathbb A}=(A_{1},...,A_{n})$ is a $n$-tuple of positive definite matrices such that $0<m\leq A_{i}\leq M\, (i=1,\cdots,n)$ for some scalars $m< M$ and $\omega=(w_{1},\cdots,w_...

In this paper, the equivalency between vectorial versions of fixed point theorems in cone rectangular metric spaces and scalar versions of fixed point theorems in rectangular metric spaces is presented. Moreover, some fixed point theorems for generalized contractions in cone rectangular metric spaces are provided. Theresults of this paper can be co...

In this paper, we introduce the new notion of generalized α-φ-Geraghty proximal contraction mappings and investigate the existence of the best proximity point for such mappings in complete metric spaces. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature. MSC: 47H10; 54H25;...

In this paper, first we prove some lemmas, then by using the nonlinear scalarization function, we prove that there is no difference between the topological boundedness and the ordered boundedness. As an application, a fixed point theorem which is a new version of the main result obtained by Zangenehmehr et al (Positivity, 19, 333-340, 2015), by rel...

We determine the fine spectrum of generalized upper triangle double-band matrices Δ uv over the sequence space ℓ 1 .

In this paper we consider the problem of finding norms of certain matrix operators on sequence space bvp. In fact, we consider these problems for weighted mean, and generalized Cesaro matrices on sequence space bvp.

Let $A = {({a_{n,k}})_{n,k \ge 1}}$ be a non-negative matrix. Denote by L v,p,q,F (A) the supremum of those L that satisfy the inequality $$\parallel Ax{\parallel _{v,q,F}} \ge L\parallel x{\parallel _{v,p,F}}$$ where x ⩾ 0 and x ε ℓp (v, F) and also v = (v n ) n=1∞ is an increasing, non-negative sequence of real numbers. If p = q, we use L v,p...

We prove the classical Hardy inequality in a block weighted sequence space. Also, by a nonnegative function K=K(x,y) we define a corresponding continuous case of the block sequence space. Indeed, by a nonnegative Lebesgue measurable function K on (0,∞)×(0,∞), we define L K p :=f : ∫ 0 ∞ ∫ 0 ∞ K (x,y) |f(x)| d x p d y < ∞· The space L K p equipped t...

Let A=(a n,k )n,k≥0 be a non-negative matrix. Denote by \(L_{l_{p} (w),~e_{w,q}^{\theta}}(A)\) the supremum of those L, satisfying the following inequality: where x≥0, x∈l p (w) and w=(w n ) is a decreasing, non-negative sequence of real numbers. In this paper, first we introduce the Euler weighted sequence space, \(e_{w,p}^{\theta}~(0< p < 1)\), o...

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.

The main purpose of this paper is to determine the fine spectrum of the generalized difference operator Δ uv over the sequence space c 0 . These results are more general than the fine spectrum of the generalized difference operator Δ v of P. D. Srivastava and S. Kumar [Commun. Math. Anal. 6, No. 1, 8–21 (2009; Zbl 1173.47022)].

Let A=(a n,k ) n,k≥1 and B=(b n,k ) n,k≥1 be two non-negative matrices. Denote by L v,p,q,B (A), the supremum of those L, satisfying the following inequality: ∥Ax∥ v,B(q) ≥L∥x∥ v,B(p) , where x≥0 and x∈l p (v,B) and also v=(v n ) n=1 ∞ is an increasing, non-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for L v,p,q...

In the present paper, the fine spectrum of the Zweier matrix as an operator over the weighted sequence space ℓ p (w) is examined.

Let H=(n,k)n,k≥obe a non-negative matrix. Denote by Lw,p,q(H), the supremum of those L, satisfying the following inequality: [∑ n=o∞wn[∑ k=o∞hn,kxk]q] 1/q≥L[∑k=o∞wkx kp]1/p, where x≥0,x∞lp(w), and also w=(wn) is increasing, non-negative sequence of real numbers. If p=q, we used Lw,p (H), instead of Lw,p,p(A). The purpose of this paper is to establi...

Let A=(a n,k ) n,k≥0 be a non-negative matrix. Denote by L w,p,q (A), the supremum of those L, satisfying the following inequality: ∑ n=0 ∞ w n ∑ k=0 ∞ a n,k x k q 1 q ≥L∑ k=0 ∞ w k x k p 1 p , where, x≥0 and x∈l p (w) and also w=(w n ) is a decreasing, non-negative sequence of real numbers. If p=q, then we use L w,p (A) inested of L w,p,p (A). Her...

Let 1<p<∞ and A=(a n,k ) n,k≥1 be a non-negative matrix. Denote by ∥A∥ w,p,F , the infimum of those U satisfying the following inequality: ∥Ax∥ w,p,F ≤U∥x∥ w,p,I , where x≥0 and x∈l p (w,I) and also w=(w n ) n=1 ∞ is a decreasing, non-negative sequence of real numbers. The purpose of this paper is to give a lower bound for {A∥ w,p,F , where A is a...

The purpose of this study is the problem of finding an upper bound and a lower bound of integral operators defined by $$ (Bf)(x) = \int\limits_0^\infty {b(x,y)f(y)dy,} $$ on weighted spaces. In fact, we consider certain integral operators such as Averaging, Copson and Hilbert operators on weighted Lorentz space Λ(w, p). Also, we study such cons...

In this paper we consider some matrix operators on block weighted sequence spaces l p (w, F). The problem is to find the lower bound of some matrix operators such as Hausdorff and Hilbert matrices on l p (w, F). This study is an extension of papers by G. Bennett, G.J.O. Jameson and R. Lashkaripour.

Themain goal of the present study is to give some estimations for upper bound and lower bound of some matrix operators on weighted sequence spaces d(w, p) and l p (w). We considered this problem for certain matrix operators such as Nörlund, Weighted mean, Ceasàro and Copson matrices, which is recently considered in [7–13]. Also, this study is an e...

In this paper we consider the problem of finding upper bounds of certain matrix operators such as Hausdorff, Nörlund matrix, weighted mean and summability on sequence spaces l p(w) and Lorentz sequence spaces d(w, p), which was recently considered in [9] and [10] and similarly to [14] by Josip Pecaric, Ivan Peric and Rajko Roki. Also, this study is...

This paper is concerned with the problem of finding the upper and lower bounds of matrix operators from weighted sequence spaces lp(v;I) into lp(v;F). We consider certain matrix operators such as Cesaro, Copson and Hilbert which were recently considered in (7, 8, 11, 13) on the usual weighted sequence spaces lp(v).

The purpose of this paper is finding a lower bound for summability matrix operators on sequence spaces lp(w) and Lorentz sequence spaces d(w,p) and also the sequence space e(w, ∞). Also, this study is an extension of some works of Bennett.

In this paper, we considered the problem of finding the upper bound Hausdorff matrix operator from sequence spaces lp(v) (ord(v, p)) intol p (w) (ord(w, p)). Also we considered the upper bound problem for matrix operators fromd(v, 1) intod(w, 1), and matrix operators frome(w, ∞) intoe(v, ∞), and deduce upper bound for Cesaro, Copson and Hilbert mat...

In this paper, we concern with transpose of the weighted mean matrix (This is upper triangular matrix.) on weighted sequence spaces 'p(w) and Lp(w) which is considered by the author in (8) and (9) for special case of these operator, such as Copson on '1(w) and d(w,1). Also, in a recent paper(7), the author has discovered the upper bound for the Cop...

In a recent paper [8], the author has discoverd the norm for the Cesaro, Copson and Hilbert operators on Lorentz sequence space d(w,1). The purpose of this note is to establish analogous norms for arbitrary weighted mean matrices(with non-negative entries) acting on arbitrary ‘1(w)(d(w,1)) spaces. Key Words:Norm, Weighted Mean Matrix,Weighted Seque...

The problem addressed is the exact determination of the norms of the classical Hilbert, Copson and averaging operators on weighted 'p spaces and the corresponding Lorentz sequence spaces d(w,p), with the power weighting sequence wn = n or the variant defined by w1+···+wn = n1 . Exact values are found in each case except for the averaging operator w...

The problem considered is thedetermination of of matrix operators on the spaces\ell_p(w) or d(w,p). Under fairly general conditions, thesolution is the same for both spaces and is given by the infimum of a certain sequence. Specific casesare considered, with the weighting sequence defined by w_n = 1/n^\alpha . The exactsolution is found for the Hil...