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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. Research

    A new chaotic behavior of a general model of the Henon map

    In this paper we are concerned with a general form of the Henon map as a retarded functional equation. The existence of a unique solution is proved. The continuous dependence of the solution and the local stab...

    Ahmed M. A. El-Sayed, Zaki F. E. El-Raheem and Sanaa M. Salman

    Advances in Difference Equations 2014 2014:107

    Published on: 8 April 2014

  2. Research

    Nabla discrete fractional Grüss type inequality

    Properties of the discrete fractional calculus in the sense of a backward difference are introduced and developed. Here, we prove a more general version of the Grüss type inequality for the nabla fractional ca...

    A Feza Güvenilir, Billur Kaymakçalan, Allan C Peterson and Kenan Taş

    Journal of Inequalities and Applications 2014 2014:86

    Published on: 20 February 2014

  3. Research

    Multipled fixed point theorems in cone metric spaces

    In this paper, the concept of common multipled fixed points of w-compatible nonlinear contractive maps in cone metric spaces, which are generalizations of common coupled fixed points, is introduced. A new concept...

    Hallowed Olaoluwa and Jonhson Olaleru

    Fixed Point Theory and Applications 2014 2014:43

    Published on: 18 February 2014

  4. Research

    Nonlinear biharmonic boundary value problem

    We consider the nonlinear biharmonic equation with variable coefficient and polynomial growth nonlinearity and Dirichlet boundary condition. We get two theorems. One theorem says that there exists at least one...

    Tacksun Jung and Q-Heung Choi

    Boundary Value Problems 2014 2014:30

    Published on: 4 February 2014

  5. Research

    Best proximity point results for modified Suzuki α-ψ-proximal contractions

    In this paper, we introduce a modified Suzuki α-ψ-proximal contraction. Then we establish certain best proximity point theorems for such proximal contractions in metric spaces. As an application, we deduce best p...

    Nawab Hussain, Abdul Latif and Peyman Salimi

    Fixed Point Theory and Applications 2014 2014:10

    Published on: 9 January 2014

  6. Research

    Existence of nontrivial solutions for p-Kirchhoff type equations

    In this paper, the linking theorem and the mountain pass theorem are used to show the existence of nontrivial solutions for the p-Kirchhoff equations without assuming Ambrosetti-Rabinowitz type growth conditions,...

    Chunhan Liu, Jianguo Wang and Qingling Gao

    Boundary Value Problems 2013 2013:279

    Published on: 30 December 2013

  7. Research

    A note on Caristi-type cyclic maps: related results and applications

    In this note, we first introduce the concept of Caristi-type cyclic map and present a new convergence theorem and a best proximity point theorem for Caristi-type cyclic maps. It should be mentioned that in our...

    Wei-Shih Du and Erdal Karapinar

    Fixed Point Theory and Applications 2013 2013:344

    Published on: 16 December 2013

  8. Research Article

    A nonlocal multi-point multi-term fractional boundary value problem with Riemann-Liouville type integral boundary conditions involving two indices

    In this paper, we study the existence of solutions for fractional differential equations of arbitrary order with multi-point multi-term Riemann-Liouville type integral boundary conditions involving two indices...

    Ahmed Alsaedi, Sotiris K Ntouyas, Ravi P Agarwal and Bashir Ahmad

    Advances in Difference Equations 2013 2013:369

    Published on: 13 December 2013

  9. Research

    A vaccination strategy based on linearization control techniques for fighting against epidemic diseases propagation

    This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by a SIRS (susceptible plus infected plus recovered populations) epide...

    Santiago Alonso-Quesada, Manuel De la Sen, Asier Ibeas and Raúl Nistal

    Advances in Difference Equations 2013 2013:364

    Published on: 12 December 2013

  10. Research

    An iterative method for variational inequality problems

    In this paper, we present some properties of generalized proximity operators andpropose an iterative method of approximating solutions for a class ofgeneralized variational inequalities and show its convergenc...

    Wei-Bo Guan

    Journal of Inequalities and Applications 2013 2013:574

    Published on: 5 December 2013

  11. Research

    A first-order adjoint and a second-order hybrid method for an energy output least-squares elastography inverse problem of identifying tumor location

    In this paper we investigate the elastography inverse problem of identifying cancerous tumors within the human body. From a mathematical standpoint, the elastography inverse problem consists of identifying the...

    Nathan D Cahill, Baasansuren Jadamba, Akhtar A Khan, Miguel Sama and Brian C Winkler

    Boundary Value Problems 2013 2013:263

    Published on: 2 December 2013

  12. Research

    Statistical approximation by Kantorovich-type discrete q-Betaoperators

    The aim of the present paper is to introduce a Kantorovich-type modification ofthe q-discrete beta operators and to investigate their statistical andweighted statistical approximation properties. Rates of statist...

    Vishnu Narayan Mishra, Kejal Khatri and Lakshmi Narayan Mishra

    Advances in Difference Equations 2013 2013:345

    Published on: 29 November 2013

  13. Research

    Hybrid viscosity CQ method for finding a common solution of a variational inequality, a general system of variational inequalities, and a fixed point problem

    In the literature, various iterative methods have been proposed for finding a common solution of the classical variational inequality problem and a fixed point problem. Research along these lines is performed ...

    Lu-Chuan Ceng, Sy-Ming Guu and Jen-Chih Yao

    Fixed Point Theory and Applications 2013 2013:313

    Published on: 25 November 2013

  14. Research

    Some fixed point theorems in locally p-convex spaces

    In this paper we investigate the existence of a fixed point of multivalued mapson almost p-convex and p-convex subsets of topological vectorspaces. Our results extend and generalize some fixed point theorems on t...

    Leila Gholizadeh, Erdal Karapınar and Mehdi Roohi

    Fixed Point Theory and Applications 2013 2013:312

    Published on: 25 November 2013

  15. Research

    Bounded solutions for the nonlinear wave equation

    We investigate the number of periodic weak solutions for the wave equation with nonlinearity decaying at the origin. We get a theorem which shows the existence of a bounded weak solution for this problem. We o...

    Tacksun Jung and Q-Heung Choi

    Boundary Value Problems 2013 2013:257

    Published on: 25 November 2013

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