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The purpose of this paper is to present some sufficient conditions for the existence of solutions for nonlinear matrix equations and the second-order two-point boundary value problems for nonlinear ordinary differential equations via fixed point theorem. To do this, we introduce two classes of mappings called the Suzuki–Geraghty-[Formula: see text]-[Formula: see text]-contraction mappings and generalize Suzuki-type [Formula: see text]-F-contraction mappings and establish some fixed point results for these classes of mappings. The results obtained in this work complements, extends, generalizes, and improves some known results in the literature.

In this paper, we introduce a generalized viscosity method which includes a sequence of contractive mappings for approximating solutions of fixed point problem of finitely many resolvents of a lower semi-continuous function together with a fixed point problem of countable infinite family of [Formula: see text]-Lipschitzian and quasi-pseudocontractive mappings in Hadamard spaces. We establish a strong convergence result without imposing a compactness condition of the proposed algorithm to an element in the intersection of the set of solutions of fixed point problem of finitely many resolvents of a lower semi-continuous function and fixed point problem of countable infinite family of quasi-pseudocontractive mappings. We display a numerical example to show the applicability of our main result. Our results complement and extend many recent results in literature.

In this paper, we propose a new modified relaxed inertial regularization method for finding a common solution of a generalized split feasibility problem, the zeros of sum of maximal monotone operators, and fixed point problem of two nonlinear mappings in real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the aforementioned problems without using the conventional two cases approach. In addition, we apply our convergence results to the classical variational inequality and equilibrium problems, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other existing methods in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

In this paper, we study split generalized mixed equilibrium problem and fixed point problem in real Hilbert spaces with a view to analyze an iterative method for approximating a common solution of split generalized mixed equilibrium problem and fixed point problem of an infinite family of a quasi-nonexpansive multi-valued mappings. The iterative algorithm introduced in this paper is designed in such a way that it does not require the knowledge of the operator norm. We state and prove a strong convergence result of the aforementioned problems and also give application of our main result to split variational inequality problem. Our result complements and extends some related results in literature.

In this paper, we prove some fixed point theorems for a new type of generalized contractive mappings involving [Formula: see text]-class function, [Formula: see text]-admissible type mapping and Suzuki-type mappings in the frame work of complete [Formula: see text]-metric spaces. The results obtained in this work generalize and improve some fixed point results in the literature.

In this paper, we introduce a viscosity-type proximal point algorithm comprising of a finite composition of resolvents of monotone bifunctions and a generalized asymptotically nonspreading mapping recently introduced by Phuengrattana [Appl. Gen. Topol. 18 (2017) 117–129]. We establish a strong convergence result of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a generalized asymptotically nonspreading and nonexpansive mappings, which is also a unique solution of some variational inequality problems in an Hadamard space. We apply our result to solve convex feasibility problem and to approximate a common solution of a finite family of minimization problems in an Hadamard space.