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In this paper, we propose a new modified proximal point algorithm involving fixed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm ∆-converges to a common solution between certain convex optimization and fixed point problems.

In this paper, we introduce a new modified proximal point algorithm involving fixed point iterates of nonexpansive mappings in $\operatorname{CAT}(0)$ spaces and prove that the sequence generated by our iterative process converges to a minimizer of a convex function and a fixed point of mappings.

In this paper, we prove the strong convergence theorem for split feasibility problem involving a uniformly asymptotically regular nonexpansive semigroup and a total asymptotically strict pseudocontractive mapping in Hilbert spaces. Our main results improve and extend some recent results in the literature.

We introduce a new nonlinear mapping generated by a finite family of nonexpansive mappings. Weak and strong convergence theorems are also established in the setting of a Banach space.

In this work, we establish strong convergence theorems for solving the fixed point problem of nonexpansive semigroups and strict pseudocontractions, and the zero-finding problem of maximal monotone operators in a Hilbert space. We further apply our result to the convex minimization problem and commutative semigroups. MSC: 47H09; 47H10

We investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Fréchet differentiable norm. Our results improve and extend the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results. We also point out that the condition given by Chidume-Shahzad (2010) is not satisfied in a real Hilbert space. We show that their results still are true under a new condition.