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5 Demonstratio Mathematica

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Fixed point iterations of three asymptotically pseudocontractive mappings

Rafiq A.

Demonstratio Mathematica

2013

Vol. 46, nr 3

559--569

In this paper, we establish the strong convergence for a modified three-step iterative scheme with errors associated with three mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest. Remark at the end simplifies many known results.

A generalized Ostrowski type inequality for a random variable whose probability density function belongs to L-infinity[a,b].

Rafiq A., Mir N., Zafar F.

Demonstratio Mathematica

2008

Vol. 41, nr 3

723-732

We establish here an inequality of Ostrowski type for a random variable whose probability density function belongs to L-infinity[a, b], in terms of the cumulative distribution function and expectation. The inequality is then applied to generalized beta random variable.

Strong convergence of an implicit iteration process for a finite family of quasi-contractive operators

Rafiq A.

Demonstratio Mathematica

2007

Vol. 40, nr 1

203-208

The purpose of this paper is to establish a strong convergence of an implicit iteration process to a common fixed point for a finite family of quasi-contractive operators. Our theorems give an armative response to a question raised by [Xu and Ori, Numer. Funct. Anal. Optim. 22 (2001) 767-773 ].

Some inequalities of Aczel type for Gramians in n-inner product spaces

Rafiq A., Mir N., Hussain S.

Demonstratio Mathematica

2007

Vol. 40, nr 3

609-629

Some inequalities of Aczel type for Gramians in n-inner product spaces which generalize pecaric result for n-inner product spaces are given. Applications connected to Schwartz’s inequality for n-inner product spaces are also noted.

A note on the theorem of V. Berinde

Rafiq A.

Demonstratio Mathematica

2006

Vol. 39, nr 4

863-867

V. Berinde presented convergence theorem [1] in normed spaces for Ishikawa iterations associated with Zamfirescue operators, which is an extension of the theorem of Rhoades [11]. In this note, we point out some misprints in the calculations and established new inequalities involved in the proof of the theorem. Consequently we give better estimation in proving the convergence theorem.