This paper presents an overview that aims to discuss a brief historical account of the
development through the definitions and comparison of weaker forms of continuity notions in …

We extend the Kannan contraction principle and obtain a result that holds for both
contractive and non-expansive map**s. Such map**s admit multiple fixed-points and …

In this paper we prove a theorem which ensures the existence of a unique fixed point and is
applicable to contractive type map**s as well as map**s which do not satisfy any …

This paper deals with a well known open problem raised by Kannan (Bull. Calcutta Math.
Soc., 60: 71–76, 1968) and BE Rhoades (Contemp. Math., 72: 233–245, 1988) on the …

We introduce a weaker form of continuity which is a necessary and sufficient condition for
the existence of fixed points. The obtained theorems exhibit interesting fixed point–eventual …

Recently, there has been a considerable effort to obtain new solutions to the Rhoades' open
problem on the existence of contractive map**s that admit discontinuity at the fixed point …

We extend the concept of Φ-contraction map**s and introduce a condition that applies to
contraction map**s as well as nonexpansive map**s. The fixed-point sets and domains …

Recently, the Rhoades' open problem which is related to the discontinuity at fixed point of a
self-map** and the fixed-circle problem which is related to the geometric meaning of the …

In this article, we establish new fixed ellipse theorems that will provide a geometrical
perspective to the classical metric fixed point theory. Also, we provide novel fixed ellipse …

In this paper, we obtain new fixed point results with the help of various techniques
constructed by using auxiliary numbers and some family of functions. In the context of the …