Some New Observations and Results for Convex Contractions of Istratescu’s Type

Abstract

The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and quasi b-metric spaces.

A Relation-Theoretic Metrical Fixed Point Theorem for Rational Type Contraction Mapping with an Application

“…Several researchers stated various contraction conditions [3][4][5][6][7][8] for the fixed point theorem. Inspired by Turinici's [9] work, Ran-Reurings in 2004 formulate the result that there will be a fixed point of self-mappings that is applied only for those points which are comparable to each other by an order relation in partial metric space.…”

Fixed-disc results on metric spaces

“…The metric fixed-point theory was started by Banach contraction principle as a new scientific area [5]. This theory is one of the most significant research fields in nonlinear analysis (for some examples, see [1,3,4,9,13,20,30]). The Banach contraction principle based on the distance of two pairwise points d(u, v) and the distance of images of the corresponding points d( f u, f v) for all u, v ∈ X, where (X, d) is a metric space and f : X → X is a self-mapping.…”

New Results on F-Contractions in Complete Metric Spaces

“…He considered the following seven values: d( x, y), d(t x, t y), d( x, t x), d t x, t 2 x , d( y, t y), d t y, t 2 y and d t 2 x, t 2 y for all x, y ∈ X . For further details, the reader is referred to papers [4][5][6][7].…”