Abstract:

In this paper, we introduce a new class ${\cal A}$^* of 3-dimensional functions, which is a generalization of a known class ${\cal A}$, obtain a fixed point theorem for a mapping and a common fixed point theorem for a infinite family of mappings, and discuss the existence problems of fixed points for a mapping on a nonempty set with two metrics under the non-continuity and non-completeness. The obtained results generalize and improve many known conclusions.

Key words: ${\cal A}$')">Class ${\cal A}$, ${\cal A}$^*')">Class ${\cal A}$^*, (Common) Fixed point