Abba Auwalu

A Note on Banach Contraction Mapping principle in Cone Hexagonal Metric Space

In this paper, we prove fixed point theorem of a self mapping in non-normal cone hexagonal metric spaces. Our result extend and improve some recent results of Azam et al., [Banach contraction principle on cone rectangular metric spaces, Applicable Analysis and Discrete Mathematics, 3 (2), 236 241, 2009], Rashwan and Saleh [Some Fixed Point Theorems in Cone Rectangular Metric Spaces, Mathematica Aeterna, 2 (6): 573 587, 2012], Garg and Agarwal, [Banach Contraction Principle on Cone Pentagonal Metric Space, J. Adv. Studies Topol., 3 (1), 12 18, 2012], Garg, [Banach Contraction Principle on Cone Hexagonal Metric Space, Ultra Scientist, 26 (1), 97 103, 2014], and others. *Corresponding author: E-mail: abba.auwalu@neu.edu.tr, abbaauwalu@yahoo.com; Auwalu and Hincal; BJMCS, 16(1), 1-12, 2016; Article no.BJMCS.25172

The Kannan's Fixed Point Theorem in a Cone Hexagonal Metric Spaces

In this paper, we prove Kannans fixed point theorem in a cone hexagonal metric space. Our result extend and improve the recent result of Jleli and Samet (The Kannans fixed point theorem in a cone rectangular metric space, J. Nonlinear Sci. Appl., 2 (2009), 161 - 167), and many existing results in the literature. Example is given showing that our result are proper extensions of the existing ones.

Synchronal and cyclic algorithms for fixed point problems and variational inequality problems in Banach spaces

AbstractIn this paper, we study synchronal and cyclic algorithms for finding a common fixed point x∗ of a finite family of strictly pseudocontractive mappings, which solve the variational inequality 〈(γf−μG)x∗,jq(x−x∗)〉≤0,∀x∈⋂i=1NF(Ti), where f is a contraction mapping, G is an η-strongly accretive and L-Lipschitzian operator, N≥1 is a positive integer, γ,μ>0 are arbitrary fixed constants, and {Ti}i=1N are N-strict pseudocontractions. Furthermore, we prove strong convergence theorems of such iterative algorithms in a real q-uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.MSC:47H06, 47H09, 47H10, 47J05, 47J20, 47J25.We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.