Metric fixed point theory: a brief retrospective

Fixed point theory in generalized orthogonal metric space

In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.

Fixed Point Theory in $varepsilon$-connected Orthogonal Metric Space

The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some i...

Introduction To Metric Fixed Point Theory

Transfinite Methods in Metric Fixed-point Theory

This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author’s 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent exte...

Proof mining in metric fixed point theory and ergodic theory

In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach spaces.