Convergence and stability of generalized φ-weak contraction mapping in CAT(0) spaces

Abstract

Abstract:The aim of this paper is to prove some fixed point results for generalized '-weak contraction mapping and study a new concept of stability which is called comparably almost T -stable by using iterative schemes in CAT .0/ spaces.

The Comparably Almost (S,t)- Stability for Random Jungck-Type Iterative Schemes

“…

In this paper, we introduce the concept of generalized φ -weakly contractive random operators and study a new type of stability introduced by Kim [15] which is called a comparably almost stability and then prove the comparably almost (S,T)-stability for the Jungck-type random iterative schemes. Our results extend and improve the recent results in [15], [18], [32] and many others. We also give stochastic version of many important known results.

…”

“…If L(w) = 0 for each ω ∈ Ω and S = I d (identity random mapping) in the condition (2.7), then it reduces to the stochastic version of the condition (1.1). Motivated by the definition of a comparably almost stability in [15] together with the definition of (S,T)-stability in [28], we state the stochastic version of the comparably almost (S,T)-stability as follows:…”

“…In 2017, Kim [15] introduced a new concept of stability which is called comparably almost T-stability defined as: Definition 1.5. Let (X, d) be a metric space, T : X → X be a self-mapping and x 0 ∈ X.…”

Variants of R-weakly commuting mappings satisfying a weak contraction

“…In 2017, Jain et al [6] introduced a new type of inequality having cubic terms of d(x, y) that extended and generalized the results of Alber and Gueree-Delabriere [2] and others cited in the literature of fixed point theory. See [1,3,7,10,11] for more information on fixed point theory.…”