On some fixed point theorems for ordered vectorial Ciric-Presic type contractions


ÖZEKEN Ç. C. , ÇEVİK C.

JOURNAL OF ANALYSIS, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s41478-022-00504-z
  • Journal Name: JOURNAL OF ANALYSIS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Keywords: Ciric-Presic type operators, Fixed point, Riesz space, Partial ordered metric spaces, Ordered vector metric spaces, SETS
  • Gazi University Affiliated: Yes

Abstract

Banach contraction mapping principle is one of the building blocks of metric fixed point theory. Numerous generalizations of this principle have been made usually by altering the metric space with a more general space and changing the contraction conditions. In this paper, by utilizing these ways we present a fixed point theorem for ordered vectorial Ciric-Pres ic type contractions. This result extends many results in the literature such as the ones obtained for Ciric-Presic type contractions on both metric and partially ordered metric spaces. With some remarks, we emphasize that every ordered Presic and ordered Ciric-Pre sic type contractions has to be an ordered vectorial Ciric -Presic type contraction nevertheless the converse may not be true in general. In addition, with an example, we support our conclusion and also show that the results existing in the literature are not applicable to this example.