In this paper, we introduce a new iterative procedure which is constructed by the modified block hybrid projection method for solving a common solution of fixed point problems for two countable families of uniformly total quasi-φ-asymptotically nonexpansive and uniformly Lipschitz continuous mappings. Under suitable conditions, some strong convergence theorems are established in a uniformly smo...

Abstract: Let m : Σ → X be a Banach space valued countably additive vector measure. In this paper we present a procedure to construct an m -orthogonal system in the space L(m) of square integrable functions with respect to m . If the vector measure is constructed from a family of indeterminate scalar measures, it is possible to obtain a family of polynomials that is orthogonal with respect to t...

The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f -projection operator for finding a common solution of fixed-point problem of a totally quasi-φ-asymptotically nonexpansivemapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong converg...

The purpose of this paper is first to introduce the concept of total quasi-φ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a count...