Sami Atif Theyab Shukri

We establish fixed point existence and convergence theorems for mappings of asymptotically nonexpansive type (ANT) in CATp(0) metric spaces for p ≥ 2. We extend these results to nonself ANT mappings via a projection-based iterative scheme. Additionally, we derive weak and strong convergence theorems for asymptotically quasi-nonexpansive type (AQNT) mappings, generalizing results from standard CAT(0) metric and Banach spaces.

This paper introduces a metric version of Goebel’s definition for uniformly non-square Banach spaces. We show that such spaces with a characteristic of convexity strictly less than one possess the uniform normal structure property. This property implies property (R), which in turn is equivalent to reflexivity in Banach spaces. As an application, we explore conditions for finding fixed points of a continuous mapping of uniformly k-Lipschitzian type on a complete bounded uniformly non-square metric space.

In this work, we investigate the closest point theorem in complete CATp(0) metric spaces for p ≥ 2. As an application, an extension of the Banach Contraction Principle for best proximity points is obtained.

In this work, we obtain fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in complete CATp(0) metric spaces for p ≥ 2. Our results extend and improve many results in the literature.

In this work, some geometrical properties of Hilbert spaces are investigated in lp spaces, for p ≥ 2. As an application, we obtain an extension of the Banach Contraction Principle for best proximity points. The case of nonexpansive mappings is also discussed.

In this paper, based on some geometrical properties of CATp(0) spaces, for p ≥ 2, we obtain two fixed point results for monotone multivalued nonexpansive mappings and proximally monotone nonexpansive mappings. Which under some assumptions, reduce to coincide and generalize a fixed point result for monotone nonexpansive mappings. This work is a continuity of the previous work of Ran and Reurings, Nieto and Rodríguez-López done for monotone contraction mappings.

In this work, we study existence and convergence of best proximity points of a cyclic contraction mapping in a complete CATp(0) metric space, with p ≥ 2. The case of coupled best proximity points of a pair of cyclic contraction mappings is also discussed. As an application, we provide sufficient conditions to obtain an extension of the Banach Contraction Principle for coupled fixed points.