Generalizations of Kannan and Reich Fixed Point Theorems, Using Sequentially Convergent Mappings and Subadditive Altering Distance Functions

Some fixed point theorems by altering distance functions

Fixed point theorems for Kannan-type maps

for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

Common fixed points for a pair of mappings in $b$-Metric spaces via digraphs and altering distance functions

In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying some generalized contractive type conditions in $b$-metric spaces endowed with graphs and altering distance functions. Finally, some examples are provided to justify the validity of our results.

Fixed point theorems for $alpha$-contractive mappings

In this paper we prove existence the common fixed point with different conditions for $alpha-psi$-contractive mappings. And generalize weakly Zamfirescu map in to modified weakly Zamfirescu map.

Cone metric spaces and fixed point theorems of T -Kannan contractive mappings

The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T -Kannan type mappings on complete cone metric spaces depended on another function.