On Multi -Valued Contractive Mappings and Fixed-Point Theorems in Complete D^*-Symmetric Spaces

The importance of fixed-point theory has encouraged many authors to consider it in various types of single and multi-valued mappings and it is gained tremendous implementations in many fields of pure and applied mathematics and other sciences; also, this theory for multi-valued contraction mappings has acquired formidable implementation in venous sciences such as optimization, economics, deferential equations and control theory. Therefore, the main motivation of present manuscript is to study and verify various fixed-point theorems for multi-valued contraction maps, as well existence of common fixed points and uniqueness for occasionally-weakly compatible maps has been proved under influence some certain generalized multi-valued weak-contractive conditions in the context of new extended symmetric space namely, -symmetric space which is extension of -metric and G-symmetric spaces. Our major outcomes which are related to these kinds of fixed-point theorems for multi-valued contraction maps are extensions of the various outcomes existing in the literature. Additionally, suitable examples that support our major outcomes have been prepared