Orthogonal cone A-metric spaces

In this thesis work, orthogonal cone metric space and A-metric space structure are considered together and orthogonal cone A-metric space structure is obtained. In addition, some fixed point theorems for orthogonal contraction mappings defined on this structure are stated and proved. This thesis consists of nine chapters. In the first chapter, a detailed literature review is made regarding the studies on the generalization of metric spaces; in the second section, definitions of various metric structures leading to the definition of the A-metric structure are given; in the third section, general definitions, theorems and examples are given about A-metric spaces; in the fourth section, basic definitions, theorems and examples are given about cone A-metric spaces; in the fifth section, basic definitions, theorems and examples are given about orthogonal cone metric spaces; in the sixth section, the orthogonal cone A-metric space structure is established and basic definitions and auxiliary theorems are given on this structure; In the seventh section, the existence of fixed points for some contraction mappings defined on the orthogonal cone A-metric space structure is examined and exemplified; in the eighth section, a partial ordering relation is defined on the orthogonal cone A-metric structure and the fixed point theorems given in the seventh section are reshaped and proven by means of this ordering relation; in the last section, the results obtained from this study are given and recommendations are made.