EXISTENCE OF FIXED POINT FOR NONLINEAR OPERATOR IN PARTIALLY ORDERED METRIC SPACES

Yan Sun; Ravi P. Agarwal

Yan Sun Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
Ravi P. Agarwal Department of Mathematics, Texas A M University Blvd., MSC 172 Kingsville, Texas 78363-8202, U.S.A.

Article ID: 2406

Keywords: weakly regular cone; fixed point; contractive mappings; existence

Abstract

In this article, first we introduce new notions of a contractive mapping and establish some fixed point theorems for the contractive mapping in the setting of LG-complete LG-metric spaces. Further, we establish a new criterion between weakly regular cone and normal cone, and we also obtain a fixed point result in the same LG-complete LG-metric spaces by making use of analysis technique. Later, we give some examples to illustrate the valid of our main results.

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