In this paper, we introduce two new classes of mappings known as λ-enriched strictly pseudocontractive mappings and ΦT-enriched Lipshitizian mappings in the setup of a real Banach space. In addition, a new modified mixed-type Ishikawa iteration scheme was constructed, and it was proved that our iteration method converges strongly to the common fixed points of finite families of the above mappings in the framework of a real uniformly convex Banach space. Moreover, we provided a non-trivial example to support our main result. Our results extend and generalize several results existing in the literature.

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In this paper, an iterative scheme for finding common solutions of the set of fixed points for a pair of asymptotically quasi-nonexpansive mapping and the set of minimizers for the minimization problem is constructed. Using the idea of the jointly demicloseness principle, strong convergence results are achieved without imposing any compactness condition on the space or the operator. Our results improve, extend and generalize many important results in the literature.

The main purpose of this paper is to introduce and study some viscosity-type proximal point algorithms for approximating a common solution of monotone inclusion problem and fixed point problem. We obtained strong convergence of the proposed algorithms to a common solution of minimization problem and fixed point problem for a generalized asymptotically nonexpansive mapping which is also a unique solution of some variational inequality problems in Hadamard spaces. Our results extend and complement some recent results in this direction.

In this manuscript, we establish a novel class of nonlinear mappings called β-enriched Suzuki generalized multivalued non-expansive mappings and prove a new existence of common fixed points for a commuting pair comprising an enriched single-valued and an enriched multivalued mapping both satisfying condition (C) in the setup of a uniformly convex Banach space. Further, weak and strong convergence results are obtained for an infinite family of this new class of mappings in the framework of uniformly convex Banach spaces. A nontrivial numerical example is presented to validate the main results of this paper. Our results extend, improve and generalize many well known results currently in literature.

We propose a three-step iteration scheme of hybrid mixed-type for three total asymptotically nonexpansive self mappings and three total asymptotically nonexpansive nonself mappings. In addition, we establish some weak convergence theorems of the scheme to the common fixed point of the mappings in uniformly convex Banach spaces. Our results extend and generalize numerous results currently in literature.

In this paper, new iterative schemes called Jungck-DI-Noor random iterative scheme and Jungck-DI-SP random iterative scheme are introduced and studied. Also, stability and convergence results were obtained without necessarily imposing sum conditions on the countably finite family of the control sequences and injectivity condition on the operators, which makes our schemes to be more desirable in applications than the ones studied in this paper and several others currently in literature.