Implicit Mann fixed point iterations for pseudo-contractive mappings

Suzuki-type fixed point theorems for generalized contractive mappings‎ ‎that characterize metric completeness

‎Inspired by the work of Suzuki in‎ ‎[T. Suzuki‎, ‎A generalized Banach contraction principle that characterizes metric completeness‎, Proc‎. ‎Amer‎. ‎Math‎. ‎Soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of Geraghty in [M.A‎. ‎Geraghty‎, ‎On contractive mappings‎, ‎Proc‎. ‎Amer‎. ‎Math‎. ‎Soc., ‎40 (1973)‎, ‎604--608]‎an...

Strong convergence of variational inequality problem Over the set of common fixed points of a family of demi-contractive mappings

In this paper, by using the viscosity iterative method and the hybrid steepest-descent method, we present a new algorithm for solving the variational inequality problem. The sequence generated by this algorithm is strong convergence to a common element of the set of common zero points of a finite family of inverse strongly monotone operators and the set of common fixed points of a finite family...

Modified Noor iterations for infinite family of strict pseudo-contraction mappings

Firmly pseudo-contractive mappings and fixed points

We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.

Approximating fixed points of nonexpansive mappings and solving systems of variational inequalities

‎A new approximation method for the set of common fixed points of‎ ‎nonexpansive mappings and the set of solutions of systems of‎ ‎variational inequalities is introduced and studied‎. ‎Moreover‎, ‎we‎ ‎apply our main result to obtain strong convergence theorem to a‎ ‎common fixed point of a nonexpannsive mapping and solutions of ‎a ‎system of variational inequalities of an inverse strongly mono...