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Recent Advances in Operator Equations, Boundary Value Problems, Fixed Point Theory and Applications, and General Inequalities

This thematic series originates from the International Conference on the Theory, Methods and Applications of Nonlinear Equations which was held in December 2012 in Kingsville, TX-USA and was organized by the Department of Mathematics at the Texas A&M University-Kingsville.

Edited by: Ravi Agarwal, Shusen Ding, Billur Kaymakcalan, Dumitru Motreanu and Anthony To Ming Lau

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  1. In this paper, we propose a new model for segmentation of both gray-scale and color images. This model is inspired by the GAC model, the region-scalable fitting model, the weighted bounded variation model and ...

    Authors: Dazhi Zhang, Jiebao Sun, Zhichang Guo and Yanli Zhai
    Citation: Journal of Inequalities and Applications 2013 2013:556
  2. The purpose of this paper is to establish some coupled coincidence point theorems for generalized nonlinear contraction mappings with the mixed g-monotone property in the framework of metric spaces endowed with p...

    Authors: Jong Kyu Kim and Sumit Chandok
    Citation: Fixed Point Theory and Applications 2013 2013:307
  3. We investigate multiple solutions for the Hamiltonian system with singular potential nonlinearity and periodic condition. We get a theorem which shows the existence of the nontrivial weak periodic solution for...

    Authors: Tacksun Jung and Q-Heung Choi
    Citation: Journal of Inequalities and Applications 2013 2013:545
  4. In this paper, we develop a multi-model adaptive control strategy to be applied on delay compensation schemes for stable/unstable LTI MIMO systems. The only requirement is that the delay should be bounded and ...

    Authors: J Herrera, A Ibeas, M de la Sen, S Alcántara and S Alonso-Quesada
    Citation: Advances in Difference Equations 2013 2013:331
  5. We study oscillatory behavior of a class of second-order differential equations with damping under the assumptions that allow applications to retarded and advanced differential equations. New theorems extend a...

    Authors: Xiaoling Fu, Tongxing Li and Chenghui Zhang
    Citation: Advances in Difference Equations 2013 2013:326
  6. A Newton-Kantorovich convergence theorem of a new modified Halley’s method family is established in a Banach space to solve nonlinear operator equations. We also present the main results to reveal the competen...

    Authors: Rongfei Lin, Yueqing Zhao, Zdeněk Šmarda, Qingbiao Wu and Yasir Khan
    Citation: Advances in Difference Equations 2013 2013:325
  7. In this paper, we consider a Lagrange-Galerkin scheme to approximate a two-dimensional fluid-structure interaction problem. The equations of the system are the Navier-Stokes equations in the fluid part, couple...

    Authors: Jorge San Martín, Jean-François Scheid and Loredana Smaranda
    Citation: Boundary Value Problems 2013 2013:246
  8. In this paper, let X be a uniformly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We introduce and consider three-step Mann iterations for finding a common solution ...

    Authors: Lu-Chuan Ceng and Ching-Feng Wen
    Citation: Journal of Inequalities and Applications 2013 2013:539
  9. This work develops Feynman-Kac formulae for switching diffusion processes. It first recalls the basic notion of a switching diffusion. Then the desired stochastic representations are obtained for boundary valu...

    Authors: Nicholas A Baran, George Yin and Chao Zhu
    Citation: Advances in Difference Equations 2013 2013:315
  10. The purpose of this paper is to present an iterative method for finding a common element of the set of solutions for an equilibrium problem and the set of common fixed points for a countably infinite family of...

    Authors: Jong Kyu Kim and Nguyen Buong
    Citation: Fixed Point Theory and Applications 2013 2013:286
  11. We show that the fixed point methods allow to investigate Ulam’s type stability of additivity quite efficiently and precisely. Using them we generalize, extend and complement some earlier classical results con...

    Authors: Janusz Brzdęk
    Citation: Fixed Point Theory and Applications 2013 2013:285
  12. In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our re...

    Authors: Zenn-Tsun Yu and Lai-Jiu Lin
    Citation: Fixed Point Theory and Applications 2013 2013:283
  13. We first introduce a new concept of b-dislocated metric space as a generalization of dislocated metric space and analyze different properties of such spaces. A fundamental result for the convergence of sequences ...

    Authors: Nawab Hussain, Jamal Rezaei Roshan, Vahid Parvaneh and Mujahid Abbas
    Citation: Journal of Inequalities and Applications 2013 2013:486
  14. Very recently, some authors discovered that some fixed point results in thecontext of a G-metric space can be derived from the fixed point resultsin the context of a quasi-metric space and hence the usual metric ...

    Authors: Leila Gholizadeh and Erdal Karapınar
    Citation: Journal of Inequalities and Applications 2013 2013:457
  15. Very recently, Samet et al. and Jleli and Samet reported that most of fixed point results in the context of G-metric space, defined by Sims and Zead, can be derived from the usual fixed point theorems on the usua...

    Authors: Mehdi Asadi, Erdal Karapınar and Peyman Salimi
    Citation: Journal of Inequalities and Applications 2013 2013:454
  16. In this paper, we introduce the concept of generalized convex contractions and give some results about approximate fixed points of the contractions on metric spaces. By providing some examples, we show that ou...

    Authors: Mehdi Amir Miandaragh, Mihai Postolache and Shahram Rezapour
    Citation: Fixed Point Theory and Applications 2013 2013:255
  17. Wardowski (Fixed Point Theory Appl. 2012:94, 2012, doi:10.1186/1687-1812-2012-94) introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn...

    Authors: Mujahid Abbas, Basit Ali and Salvador Romaguera
    Citation: Fixed Point Theory and Applications 2013 2013:243
  18. By applying an iterative technique, a necessary and sufficient condition is obtained for the existence of the unique solution of nonlinear fractional differential equations involving two Riemann-Liouville deri...

    Authors: Guotao Wang, Sanyang Liu, Dumitru Baleanu and Lihong Zhang
    Citation: Advances in Difference Equations 2013 2013:280