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Thematic series on Nonlinear Analysis and Optimization

The 2013 International Conference on Nonlinear Analysis and Optimization (ICNAO2013) was successfully held at National Sun Yat-sen University, Kaohsiung, Taiwan on December 20-22 2013. There were over 80 plenary/invited/contributed talks in various topics of nonlinear analysis, optimization and their applications.

Edited by: Anthony To Ming Lau, Ngai-Ching Wong, Hong-Kun Xu and Jen-Chih Yao

  1. Research

    Strong and total Fenchel dualities for robust convex optimization problems

    In this paper, we present some strong and total Fenchel dualities for convex programming problems with data uncertainty within the framework of robust optimization in locally convex Hausdorff vector spaces. By...

    Mengdan Wang, Donghui Fang and Zhe Chen

    Journal of Inequalities and Applications 2015 2015:70

    Published on: 26 February 2015

  2. Research

    Minimax problems under hierarchical structures

    We discuss the minimax problems for set-valued mappings with several hierarchical structures, and scalar hierarchical minimax theorems, hierarchical minimax theorems, hierarchical minimax inequalities for set-...

    Yen-Cherng Lin

    Journal of Inequalities and Applications 2015 2015:57

    Published on: 19 February 2015

  3. Research

    A viscosity approximation method for weakly relatively nonexpansive mappings by the sunny nonexpansive retractions in Banach spaces

    In this paper, we introduce a new viscosity approximation method by using the shrinking projection algorithm to approximate a common fixed point of a countable family of nonlinear mappings in a Banach space. U...

    Chin-Tzong Pang, Eskandar Naraghirad and Ching-Feng Wen

    Journal of Inequalities and Applications 2015 2015:36

    Published on: 3 February 2015

  4. Research

    Iterative methods for triple hierarchical variational inequalities with mixed equilibrium problems, variational inclusions, and variational inequalities constraints

    In this paper, we introduce and analyze a multi-step hybrid steepest-descent extragradient algorithm and multi-step composite Mann-type viscosity iterative algorithm for finding a solution of triple hierarchic...

    Lu-Chuan Ceng, Yen-Cherng Lin and Ching-Feng Wen

    Journal of Inequalities and Applications 2015 2015:16

    Published on: 15 January 2015

  5. Research

    Ergodicity of the implicit midpoint rule for nonexpansive mappings

    We prove a mean ergodic theorem for the implicit midpoint rule for nonexpansivemappings in a Hilbert space. We obtain weak convergence for the general case andstrong convergence for certain special cases.

    Hong-Kun Xu, Maryam A Alghamdi and Naseer Shahzad

    Journal of Inequalities and Applications 2015 2015:4

    Published on: 6 January 2015

  6. Research

    Extragradient method for convex minimization problem

    In this paper, we introduce and analyze a multi-step hybrid extragradient algorithm by combining Korpelevich’s extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann...

    Lu-Chuan Ceng, Yeong-Cheng Liou and Ching-Feng Wen

    Journal of Inequalities and Applications 2014 2014:444

    Published on: 4 November 2014

  7. Research

    Existence theorems for relaxed η-α pseudomonotone and strictly η-quasimonotone generalized variational-like inequalities

    In this paper, we prove the existence of solutions for a variational-like inequality and a generalized variational-like inequality in the relaxed η-α pseudomonotone and strictly η-quasimonotone cases in Banach sp...

    Areerat Arunchai, Somyot Plubtieng and Ching-Feng Wen

    Journal of Inequalities and Applications 2014 2014:442

    Published on: 4 November 2014

  8. Research

    Multi-step iterative algorithms with regularization for triple hierarchical variational inequalities with constraints of mixed equilibria, variational inclusions, and convex minimization

    In this paper, we introduce and analyze a relaxed iterative algorithm by virtue of Korpelevich’s extragradient method, the viscosity approximation method, the hybrid steepest-descent method, the regularization...

    Lu-Chuan Ceng, Ching-Feng Wen and Cheng Liou

    Journal of Inequalities and Applications 2014 2014:414

    Published on: 16 October 2014

  9. Research

    Barnes-type Peters polynomial with umbral calculus viewpoint

    In this paper, we consider the Barnes-type Peters polynomials. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and s...

    Dae San Kim, Taekyun Kim, Hyuck In Kwon, Toufik Mansour and Jongjin Seo

    Journal of Inequalities and Applications 2014 2014:324

    Published on: 22 August 2014