Recent Trends on Fixed Point Theory and its Applications

This special issue hosts select papers presented in ICAAA2012-Istanbul. This issue is focused on recent trends and new ideas in the area of fixed point theory, its applications and related topics.

Edited by: Vatan Karakaya andYasar Sozen

Strong convergence of a modified iterative algorithm for hierarchical fixed point problems and variational inequalities

This article aims to deal with a new modified iterative projection method for solving a hierarchical fixed point problem. It is shown that under certain approximate assumptions of the operators and parameters,...

Authors: Yuanheng Wang and Wei Xu

Citation: Fixed Point Theory and Applications 2013 2013:121

Content type: Research Published on: 7 May 2013
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Data dependence results of new multi-step and S-iterative schemes for contractive-like operators

In this paper, we prove that the convergence of a new iteration and S-iteration can be used to approximate the fixed points of contractive-like operators. We also prove some data dependence results for these n...

Authors: Faik Gürsoy, Vatan Karakaya and Billy E Rhoades

Citation: Fixed Point Theory and Applications 2013 2013:76

Content type: Research Published on: 28 March 2013
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Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces

Authors: Wasfi Shatanawi and Mihai Postolache

Citation: Fixed Point Theory and Applications 2013 2013:54

Content type: Research Published on: 12 March 2013
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The new modified Ishikawa iteration method for the approximate solution of different types of differential equations

In this article, the new Ishikawa iteration method is presented to find the approximate solution of an ordinary differential equation with an initial condition. Additionally, some numerical examples with initi...

Authors: Necdet Bildik, Yasemin Bakır and Ali Mutlu

Citation: Fixed Point Theory and Applications 2013 2013:52

Content type: Research Published on: 12 March 2013
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Fixed point results for $G^{m}$ -Meir-Keeler contractive and $G - (α, ψ)$ -Meir-Keeler contractive mappings

Authors: Nawab Hussain, Erdal Karapınar, Peyman Salimi and Pasquale Vetro

Citation: Fixed Point Theory and Applications 2013 2013:34

Content type: Research Published on: 21 February 2013
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On pointwise and uniform statistical convergence of order α for sequences of functions

In this paper, we introduce the concepts of pointwise and uniform statistical convergence of order α for sequences of real-valued functions. Furthermore, we give the concept of an α-statistically Cauchy sequence ...

Authors: Muhammed Çinar, Murat Karakaş and Mikail Et

Citation: Fixed Point Theory and Applications 2013 2013:33

Content type: Research Published on: 18 February 2013
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The variational iteration method for fuzzy fractional differential equations with uncertainty

In this paper the variational iteration method is used to solve the fractional differential equations with a fuzzy initial condition. We consider a differential equation of fractional order with uncertainty an...

Authors: Ekhtiar Khodadadi and Ercan Çelik

Citation: Fixed Point Theory and Applications 2013 2013:13

Content type: Research Published on: 18 January 2013
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On the strong convergence of a modified S-iteration process for asymptotically quasi-nonexpansive mappings in a $CAT (0)$ space

In this paper, we give strong convergence theorems for the modified S-iteration process of asymptotically quasi-nonexpansive mappings on a

Authors: Aynur Şahin and Metin Başarır

Citation: Fixed Point Theory and Applications 2013 2013:12

Content type: Research Published on: 16 January 2013
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Linear and nonlinear abstract elliptic equations with VMO coefficients and applications

In this paper, maximal regularity properties for linear and nonlinear elliptic differential-operator equations with VMO (vanishing mean oscillation) coefficients are studied. For linear case, the uniform separabi...

Authors: Veli B Shakhmurov

Citation: Fixed Point Theory and Applications 2013 2013:6

Content type: Research Published on: 9 January 2013
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