Saad Elshabrawy | Damietta University (original) (raw)
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Papers by Saad Elshabrawy
Journal of Inequalities and Applications, 2014
In this paper we determine the fine spectrum of the generalized difference operator a,b defined b... more In this paper we determine the fine spectrum of the generalized difference operator a,b defined by a lower triangular double-band matrix over the sequence space c 0 . The class of the operator a,b contains as special cases many operators that have been studied recently in the literature. Illustrative examples showing the advantage of the present results are also given. MSC: Primary 47A10; secondary 47B37
The purpose of this paper is threefold: first to mainly review several recent results concerning ... more The purpose of this paper is threefold: first to mainly review several recent results concerning the fine spectrum of the operator ∆v over the sequence spaces c and lp, where 1 < p < ∞; second to provide some new results concerning the residual spectrum and the continuous spectrum of the operator ∆ v over the sequence spaces c and l p ; and third to modify the definition of the operator ∆v and to determine the fine spectrum of the modified operator over the sequence spaces c and lp, where 1 < p < ∞. Also, it may be helpful to provide some comments and examples to support our results.
In this paper we examine the fine spectrum of the generalized difference operator Δa,bΔa,b over t... more In this paper we examine the fine spectrum of the generalized difference operator Δa,bΔa,b over the sequence space cc. The boundedness of the operator Δa,bΔa,b has been proved. Also, the norm of this operator has been found. The class of the operator Δa,bΔa,b includes some other special cases such as the generalized difference operator B(r,s)B(r,s) introduced by Altay and Başar in 2005. Our results not only generalize the corresponding results in the existing literature, but also give results for some more operators.
Thai Journal of …, 2012
In the paper by Srivastava and Kumar [P.D. Srivastava, S. Kumar, Thai J. Math. 8 (2) (2010) 221-2... more In the paper by Srivastava and Kumar [P.D. Srivastava, S. Kumar, Thai J. Math. 8 (2) (2010) 221-233], the authors have introduced the lower triangular double-band matrix ∆ v as an operator on the sequence space l 1 and studied the spectrum and fine spectrum of this operator over l
Journal of Inequalities and Applications, 2014
In this paper we determine the fine spectrum of the generalized difference operator a,b defined b... more In this paper we determine the fine spectrum of the generalized difference operator a,b defined by a lower triangular double-band matrix over the sequence space c 0 . The class of the operator a,b contains as special cases many operators that have been studied recently in the literature. Illustrative examples showing the advantage of the present results are also given. MSC: Primary 47A10; secondary 47B37
The purpose of this paper is threefold: first to mainly review several recent results concerning ... more The purpose of this paper is threefold: first to mainly review several recent results concerning the fine spectrum of the operator ∆v over the sequence spaces c and lp, where 1 < p < ∞; second to provide some new results concerning the residual spectrum and the continuous spectrum of the operator ∆ v over the sequence spaces c and l p ; and third to modify the definition of the operator ∆v and to determine the fine spectrum of the modified operator over the sequence spaces c and lp, where 1 < p < ∞. Also, it may be helpful to provide some comments and examples to support our results.
In this paper we examine the fine spectrum of the generalized difference operator Δa,bΔa,b over t... more In this paper we examine the fine spectrum of the generalized difference operator Δa,bΔa,b over the sequence space cc. The boundedness of the operator Δa,bΔa,b has been proved. Also, the norm of this operator has been found. The class of the operator Δa,bΔa,b includes some other special cases such as the generalized difference operator B(r,s)B(r,s) introduced by Altay and Başar in 2005. Our results not only generalize the corresponding results in the existing literature, but also give results for some more operators.
Thai Journal of …, 2012
In the paper by Srivastava and Kumar [P.D. Srivastava, S. Kumar, Thai J. Math. 8 (2) (2010) 221-2... more In the paper by Srivastava and Kumar [P.D. Srivastava, S. Kumar, Thai J. Math. 8 (2) (2010) 221-233], the authors have introduced the lower triangular double-band matrix ∆ v as an operator on the sequence space l 1 and studied the spectrum and fine spectrum of this operator over l