Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition

By Ismat Beg, Mujahid Abbas. 2006

174 citations recorded by the source corpus.

We prove the existence of coincidence point and common fixed point for mappings satisfying generalized weak contractive condition. As an application, related results on invariant approximation are derived. Our results generalize various known results in the literature.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/acba31d529040a0f9da93b995ee411e0755a3d06

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Nawab Hussain
2. Ljubomir Ciric
3. Nenad Cakic
4. Binayak S. Choudhury
5. Nikhilesh Metiya
6. Mujahid Abbas
7. G. Jungck

In Geometry and Topology

1. Nawab Hussain
2. Ljubomir Ciric
3. Mujahid Abbas
4. Nikhilesh Metiya
5. Binayak S. Choudhury
6. Nenad Cakic
7. G. Jungck
8. Bessem Samet

Citations in the corpus

• Common fixed point results for noncommuting mappings without continuity in cone metric spaces (2008, background): “For a survey of coincidence point theory, its applications, comparison of different contractive conditions and related results, we refer to [1,6,9,10] and references contained therein.”
• Common fixed points for Ćirić type $f$-weak contraction with applications (2010, background): “Our results improve and extend the recent common fixed point results of Al-Thagafi and Shahzad [2], [3], Beg and Abbas [5], Chen and Li [10], Ćirić [11], Das and Naik [15], Jungck [19], Jungck and Hussain [21], O’Regan and Hussain [21], Pant [25], Pathak and Hussain [28], and Song [32]”
• Fixed points of weak contractions in cone metric spaces (2010, result): “Weak inequalities of the above type have been used to establish fixed point results in a number of subsequent works, some of which are noted in [8–12].”
• FIXED POINT THEOREMS FOR GENERALIZED WEAKLY CONTRACTIVE MAPPINGS (2009, unknown): “[17, 27, 7, 9]).”
• SOME RESULTS ON WEAKLY CONTRACTIVE MAPS (2012, unknown): “[4] Let (X, d) be a metric space and let f be a weakly contractive mapping with respect to g, that is, ψ(d(fx, fy)) ≤ ψ(d(gx, gy))− φ(d(gx, gy)), for some ψ ∈ Ψ and φ ∈ Φ and all x, y ∈ X.”