3: Paper Source
PDF document

Paper's Title:

**
Robust Error Analysis of Solutions to Nonlinear Volterra Integral Equation in L**^{p} Spaces

** **
Author(s):

**Hamid Baghani, Javad Farokhi-Ostad and Omid Baghani**

Department of Mathematics, Faculty of
Mathematics,

University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan,

Iran.

E-mail:
h.baghani@gmail.com

Department of Mathematics, Faculty of
Basic Sciences,

Birjand University of Technology, Birjand,

Iran.

E-mail: j.farrokhi@birjandut.ac.ir

Department of Mathematics and Computer
Sciences,

Hakim Sabzevari University, P.O. Box 397, Sabzevar,

Iran.

E-mail:
o.baghani@gmail.com

Abstract:

In this paper, we propose a novel strategy for proving an
important inequality for a contraction integral equations. The obtained inequality allows us to express our iterative algorithm using a "for
loop" rather than a "while loop". The main tool used in this paper
is the fixed point theorem in the Lebesgue space. Also, a numerical example shows the efficiency
and the accuracy of the proposed scheme.

3: Paper Source
PDF document

Paper's Title:

**
Operators On Frames**

** ****
**
Author(s):

**Javad Baradaran and Zahra Ghorbani**

Department of Mathematics,

Jahrom University, P.B. 7413188941,

Jahrom,

Iran.

E-mail:
baradaran@jahromu.ac.ir

Department of Mathematics,

Jahrom University, P.B. 7413188941,

Jahrom,

Iran.

E-mail: ghorbani@jahromu.ac.ir

Abstract:

In this paper, we first show the conditions under which an operator
on a Hilbert space *H* can be represented as sum of two unitary operators. Then, it is concluded that a Riesz
basis for a Hilbert space *H* can be written as a sum of two orthonormal bases. Finally, the study proves that if
*A* is a normal maximal partial isometry on a Hilbert space *H* and if
{e_{k}}^{∞}_{k=1} is an orthonormal
basis for *H*, then {Ae_{k}}^{∞}_{k=1}
is a 1-tight frame for *H*.

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