Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

SOLUTIONS FOR THE ORDERED VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES

J. K. Kim, - Salahuddin, A. H. Dar — Mon, 19 Oct 2020 00:00:00 +0700

In this study, we consider the ordered variational inclusion problems in ordered Banach spaces involving the weak RRD-multivalued mappings. By using the technique of relaxed resolvent operators, we suggest an iterative algorithm and prove the existence of solutions of ordered variational inclusion problems. Also, we prove the convergence of the sequences generated by an iterative algorithm.

CHARACTERIZATIONS OF THE BASIC CONSTRAINT QUALIFICATION AND ITS APPLICATIONS

D. Kuroiwa, S. Suzuki, S. Yamamoto — Mon, 19 Oct 2020 00:00:00 +0700

In convex programming, the basic constraint qualification is a necessary and sufficient constraint qualification for the optimality condition. In this paper, we give characterizations of the basic constraint qualification
at each feasible solution. By using the result, we give an alternative method for checking up the basic constraint qualification at every feasible point without subdifferentials and normal cones.

HIGH CONVERGENCE ORDER SOLVERS IN BANACH SPACE

I. K. Argyros, S. George — Mon, 19 Oct 2020 00:00:00 +0700

The local convergence of an eighth order solver is established using only the first derivative for Banach space valued operators. Earlier studies have used up to the ninth order derivatives, which limit the applicability of the solver. The results are tested using numerical experiments.

SOME FIXED POINT THEOREMS OF HARDY-ROGER CONTRACTION IN COMPLEX VALUED b-METRIC SPACES

W. Chantakun, J. Prasert — Mon, 19 Oct 2020 00:00:00 +0700

The aim of this paper is to prove the existence and uniqueness of a fixed point of a mapping satisfying the Hardy-Rogers contraction in complex-valued b-metric space, we have obtained some fixed point theorems in complex-valued b-metric spaces. This work is generalized and improved some results of Hasanah \cite{DH}, and well-known results in the literature.

GENERALIZED g-TYPE EXPONENTIAL VECTOR VARIATIONAL INEQUALITY PROBLEMS

- Salahuddin — Mon, 19 Oct 2020 00:00:00 +0700

In this works, we introduce a class of {\it generalized $g$-type exponential vector variational inequality problems} in Euclidean spaces and define $\alpha_g$-relaxed exponentially $(\tau,\mu)$-monotone mapping. By utilizing KKM-mapping and Nadler's theorem with $\alpha_g$-relaxed exponentially $(\tau,\mu)$-monotone mapping, we prove that the existence theorems of {\it generalized $g$-type exponential vector variational inequality problems}.

REMARKS ON THE BETTER ADMISSIBLE MULTIMAPS

S. Park — Mon, 19 Oct 2020 00:00:00 +0700

For a quite long period, we investigated the better admissible class $\f{B}$ of multimaps on abstract convex spaces. In a paper of Liu et al. [1] in 2010, an extended class $\f{B}^+$ is introduced and fixed point theorems for maps in such class are proved. As a consequence, they deduce fixed point theorems on abstract convex $\Phi$-spaces. However, we note that $\f{B} = \f{B}^+$ and all results in [1] are known by the present author.