S.L. Singh, Department of Mathematics, Gurukula Kangri University, Hardwar, India, and 21, Govind Nagar, Rishikesh 249201, India; email: vedicmri@gmail.com

Rajendra Pant, Department of Mathematics, S.P.R.C. Post Graduate College, Rohalki-Kishanpur, Hardwar, India; email: pant.rajendra@gmail.com

Abstract/Résumé:

We obtain fixed and common point theorems generalizing fixed point theorems of W. A. Kirk and T. Suzuki for Banach and Meir–Keeler type asymptotic contractions.

Nous démontrons des théorèmes de points fixes et de points communs qui généralisent des théorèmes de points fixes du type de Banach et de Meir–Keeler pour les contractions asymptotiques.

Keywords: Banach contraction, Meir–Keeler type asymptotic contraction, asymptotic contraction, fixed point

AMS Subject Classification: Fixed-point and coincidence theorems 54H25

PDF(click to download): Remarks on some recent fixed point theorems

Simeon Reich, Department of Mathematics, The Technion–Israel Institute of Technology, 32000 Haifa, Israel; email: sreich@tx.technion.ac.il

Alexander J. Zaslavski, Department of Mathematics, The Technion–Israel Institute of Technology, 32000 Haifa, Israel; email: ajzasl@tx.technion.ac.il

Abstract/Résumé:

Let \(K\) be a bounded, closed and convex subset of a Banach space \(X\). We show that the iterates of a typical element (in the sense of Baire category) of a class of nonexpansive mappings which take \(K\) to \(X\) converge uniformly on \(K\) to the unique fixed point of this typical element.

Soit \(K\) un sous-ensemble borné, fermé et convexe d’un espace de Banach \(X\). Nous démontrons que les itérés d’un élément typique (au sens des catégories de Baire) d’une classe d’applications non-expansives de \(K\) dans \(X\) convergent uniformément sur \(K\) vers l’unique point fixe de cet élément typique.

Keywords: Banach space, approximate fixed point, complete metric space, fixed point, generic property, iteration, nonexpansive mapping, porous set, weakly inward

AMS Subject Classification: Nonexpansive mappings; and their generalizations (ultimately compact mappings; measures of noncompactness and condensing mappings; $A$-proper mappings; $K$-set contractions; etc.) 47H09

PDF(click to download): Convergence of iterates of typical nonexpansive mappings in Banach spaces

S.L. Singh / S.N. Mishra

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Coincidence point, fixed point, multi-valued maps, weak compatibility

AMS Subject Classification: Fixed-point theorems, Set-valued maps, Fixed-point and coincidence theorems 47H10, 54C60, 54H25

PDF(click to download): Some remarks on coincidences and fixed points