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Recent Advances in Nonlinear Analysis and Optimization

This thematic series is devoted to publish the latest and significant results in nonlinear analysis and optimization. Its goals are to stimulate further research and to highlight recent advances in these fields as well as to promote, encourage, and bring together researchers in the fields of nonlinear analysis and optimization. In the last two decades, the theory of fixed point theory and related topics emerged as a rapidly growing area of research because of its applications in nonlinear analysis, optimization, economics, game theory, etc. In the recent past, many authors devoted their attention to study the fixed point theory and related topics, namely, variational inequalities, optimization and games. Many new results, including theory, methods and applications, have been developed during the recent years. This special issue aims to promote the exchange of ideas between researchers and to spread new trends in these areas.

Edited by: Qamrul Hasan Ansari, Jinlu Li and Jen-Chih Yao

  1. Research

    The common solutions of the split feasibility problems and fixed point problems

    An extraordinary split problem, which can be regarded as a superimposition of the split feasibility problem and the split fixed point problem, is considered. A superimposed algorithm is presented. The analysis...

    Abdelouahed Hamdi, Yeong-Cheng Liou, Yonghong Yao and Chongyang Luo

    Journal of Inequalities and Applications 2015 2015:385

    Published on: 8 December 2015

  2. Research

    Some fixed point results on quasi-b-metric-like spaces

    In this paper, we investigate the existence and uniqueness of a fixed point of certain operators in the setting of complete quasi-b-metric-like spaces via admissible mappings. Our results improve, extend, and uni...

    Marija Cvetković, Erdal Karapınar and Vladimir Rakocević

    Journal of Inequalities and Applications 2015 2015:374

    Published on: 2 December 2015

  3. Research

    Optimality and mixed duality in multiobjective E-convex programming

    In this paper, we consider a class of multiobjective E-convex programming problems with inequality constraints, where the objective and constraint functions are E-convex functions which were firstly introduced by...

    Guang-Ri Piao, Liguo Jiao and Do Sang Kim

    Journal of Inequalities and Applications 2015 2015:335

    Published on: 16 October 2015

  4. Research

    Some extensions for Geragthy type contractive mappings

    In this paper, we establish some fixed point theorems on some extensions of Geragthy contractive type mappings in the context of b-metric-like spaces.

    Erdal Karapınar, Hamed H Alsulami and Maha Noorwali

    Journal of Inequalities and Applications 2015 2015:303

    Published on: 26 September 2015

  5. Research

    On geodesic strongly E-convex sets and geodesic strongly E-convex functions

    In this article, geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold are extended to the so-called geodesic strongly E-convex sets and geodesic strongly E-convex functions. Some proper...

    Adem Kılıçman and Wedad Saleh

    Journal of Inequalities and Applications 2015 2015:297

    Published on: 25 September 2015

  6. Research

    A scheme for a solution of a variational inequality for a monotone mapping and a fixed point of a pseudocontractive mapping

    We introduce an iterative process which converges strongly to a common point of the solution set of a variational inequality problem for a Lipschitzian monotone mapping and the fixed point set of a continuous ...

    Mohammed Ali Alghamdi, Naseer Shahzad and Habtu Zegeye

    Journal of Inequalities and Applications 2015 2015:292

    Published on: 18 September 2015

  7. Research

    Mann-type hybrid steepest-descent method for three nonlinear problems

    We introduce a Mann-type hybrid steepest-descent iterative algorithm for finding a common element of the set of solutions of a general mixed equilibrium problem, the set of solutions of general system of varia...

    Abdul Latif, Abdulaziz SM Alofi, Abdullah E Al-Mazrooei and Jen-Chih Yao

    Journal of Inequalities and Applications 2015 2015:282

    Published on: 17 September 2015

  8. Research

    Clark’s fixed point theorem on a complete random normed module

    Motivated by the recent results in random metric theory, we establish Clark’s fixed point theorem on complete random normed modules under two kinds of topologies. When the base space of the random normed modul...

    Yujie Yang

    Journal of Inequalities and Applications 2015 2015:276

    Published on: 17 September 2015

  9. Research

    Composite viscosity methods for common solutions of general mixed equilibrium problem, variational inequalities and common fixed points

    In this paper, we introduce a new composite viscosity iterative algorithm and prove the strong convergence of the proposed algorithm to a common fixed point of one finite family of nonexpansive mappings and an...

    Lu-Chuan Ceng, Abdul Latif and Abdullah E Al-Mazrooei

    Journal of Inequalities and Applications 2015 2015:217

    Published on: 1 July 2015

  10. Research

    Strong convergence theorems for fixed point problems, variational inequality problems, and equilibrium problems

    In this paper, we first introduce an iterative algorithm for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem, and the solution set ...

    Zhangsong Yao, Yeong-Cheng Liou, Li-Jun Zhu, Ching-Hua Lo and Chen-Chang Wu

    Journal of Inequalities and Applications 2015 2015:198

    Published on: 17 June 2015

  11. Research

    A projection descent method for solving variational inequalities

    In this paper, we propose a descent direction method for solving variational inequalities. A new iterate is obtained by searching the optimal step size along a new descent direction which is obtained by the li...

    Abdellah Bnouhachem, Qamrul Hasan Ansari and Ching-Feng Wen

    Journal of Inequalities and Applications 2015 2015:143

    Published on: 23 April 2015

  12. Research

    Some elliptic system and reduction method

    We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method for the...

    Tacksun Jung and Q-Heung Choi

    Journal of Inequalities and Applications 2015 2015:96

    Published on: 14 March 2015