Fixed Point Theorems in Topological Spaces

Abstract

A couple of theorems for a pair of self-maps on a topological space have been obtained using which certain fixed point theorems in the literature for pairs of maps satisfying contractive type conditions have been deduced. In this paper our objective is to bring under a single banner various fixed point theorems for a single or a pair of self-maps on a metric or a or a topological space satisfying contractive type conditions under constrains such as the satisfaction of certain inequations by the independent variables. We have partially fulfilled our objective by generalising the results of Sastry, Naidu, Rao & Rao [4], and Sastry and Babu [2 & 3] (Theorems 1 & 2) while the latter, in turn, are generalisations of the results of Sehgal [5] and those of Khan, Swaleh & Sessa [1]. Through out this paper unless otherwise stated, IN stands for the set of all natural numbers and IR"^ for the set of all non-negative real numbers.

تم التوصل إلى نظريتين تتعلقان بالتطبيقات الذاتية على فضاء متجهاتما وذلك باستخدام بعض نظرياف النقطة الثابتة المعروفة من أجل أزواج التطبيقات التي تحقق شروطاً من النوع التقلُّصي .