ON FIXED POINT THEOREMS FOR MIXED MONOTONE OPE RATORS WITHOUT NORMALITY OF CONE

Abstract

Mixed monotone operators were introduced by Dajun Guo and
V. Lakshmikantham in 1987. Thereafter many authors have investigated these kinds of operators in Banach spaces. In 2009,
Z. Zhang- K. Wang proved the fixed point theorems for mixed
monotone operators in Banach spaces under the normal cone assumption. In this paper, we establish existence results of fixed
point for mixed monotone operators in a real Hausdorff locally
convex topological vector space without normality of cone. Our
result is an extension of Z. Zhang- K. Wang.