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In this paper, we studied a new class of nonspreading-type mappings more general than the class of strictly pseudononspreading and the class of generalized nonspreading mappings. We state and prove some strong convergence theorems of the Mann-type and Ishikawa-type algorithms for approximating fixed points of our class of mappings in Hadamard spaces.

In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

In this paper, we introduce the class of asymptotically demicontractive multivalued mappings and establish a strong convergence theorem of the modified Mann iteration to a common fixed point of a finite family of asymptotically demicontractive multivalued mappings in a complete CAT ⁢ ( 0 ) {\mathrm{CAT}(0)} space. We also give a numerical example of our iterative method to show its applicability.

In this paper, we introduce and study strong convergence of a proximal point algorithm for approximating common solution of a finite family of monotone inclusion problems and fixed point problem of a generalized demimetric mapping in complete CAT(0) spaces. An illustrative example is given to validate theoretical result obtained herein. Our results improve and generalize some well-known results in the literature.

We prove some important properties of the p-resolvent mapping recently introduced by B. J. Choi and U. C. Ji, The proximal point algorithm in uniformly convex metric spaces, Commun. Korean Math. Soc. 31 2016, 4, 845–855, in p-uniformly convex metric space. Furthermore, we introduce a modified Mann-type PPA involving nonexpansive mapping and prove that the sequence generated by the algorithm converges to a common solution of a finite family of minimization problems, which is also a fixed point of a nonexpansive mapping in the framework of a complete p-uniformly convex metric space.

In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space. We also establish weak and strong convergence theorems of the scheme. Finally, we give a numerical experiment to validate the performance of our algorithm and compare with some existing methods. Our results generalize and improve some recent results in the literature.

In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.

In this paper, we study $$\triangle$$-demiclosedness principle for asymptotically k-strictly pseudo-contractive mappings in a CAT(0) space. Also, we introduced a modified Halpern algorithm and prove its strong convergence to a fixed point of an asymptotically k-strictly pseudo-contractive mapping which is also a common solution of a finite family of monotone inclusion problems in a complete CAT(0) space. Furthermore, we applied our results to approximate a common solution of a finite family of convex minimization problem and fixed point problem for an asymptotically k-strictly pseudo-contractive mapping in a complete CAT(0) space.

In this paper, we introduce a new mapping given by a finite family of multivalued monotone mappings in a CAT(0) space. We further propose a modified Halpern-type algorithm for the mapping and prove...

In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete p-uniformly convex metric spaces. We also analyse asymptotic behaviour of the sequence generated by Halpern-type proximal point algorithm and extend it to approximate a common solution of a finite family of minimization problems in the setting of complete p-uniformly convex metric spaces. Furthermore, numerical experiments of our algorithms in comparison with other algorithms are given to show the applicability of our results.

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces.We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore,we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

In this paper, we study a modified inertial subgradient extragradient algorithm in reflexive Banach spaces and prove a strong convergence theorem for approximating common solutions of a fixed point equation of a demigeneralized mapping and a variational inequality problem of a monotone and Lipschitz mapping. Our result extends and improves important recent results announced by many authors.

The main purpose of this paper is to introduce a new mapping given by a finite family of generalized strictly pseudononspreading mappings. Also, we introduce a viscosity-type proximal point algorithm and prove its strong convergence to a common solution of a finite family of monotone inclusion problems and fixed point problem for the new mapping in a complete CAT(0) space. A numerical experiment is presented to illustrate the performance of our method as well as comparing it with some related methods in the literature. Our numerical experiment shows that our algorithm converges faster than that proposed by Takahashi and Shimoji (Math Comput Model 32:1463–1471, 2000) and Ugwunnadi et al. (Afr Mat 30(1–2):151–169, 2019).

The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.

In this paper, we introduce Halpern-type proximal point algorithm for approximating a common solution of monotone inclusion problem and fixed point problem. We obtain a strong convergence of the proposed algorithm to a common solution of finite family of monotone inclusion problem and fixed point problem for nonexpansive mappings in complete CAT(0) spaces. Nontrivial application and numerical example were given. Our results complement and extend some recent results in literature.

A new strong convergence theorem for approximation of common fixed points of family of uniformly asymptotically regular asymptotically nonexpansive mappings, which is also a unique solution of some variational inequality problem is proved in the framework of a real Banach space. The Theorem presented here extend, generalize and unify many recently announced results.

We introduce a hybrid proximal point algorithm and establish its strong convergence to a common solution of a proximal point of a lower semi-continuous mapping and a fixed point of a demicontractive mapping in the framework of a CAT(0) space. As applications of our new result, we solve variational inequality problems for these mappings on a Hilbert space. Illustrative example is given to validate theoretical result obtained herein.

We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem., 17 pages. arXiv admin note: text overlap with arXiv:1512.00243 by other authors

In this paper we prove a strong convergence of both implicit and explicit shcemes to a common fixed point of finite family of nonexpansive maps which is also a unique solution of some variational inequality problem in Banach space. The result presented here improve and unify several important results recently announced.

Let H be a real Hilbert space and T 1 , T 2 , … , T N be a family of asymptotically nonexpansive self-mappings of H with sequences { 1 + k p ( n ) i ( n ) } , such that k p ( n ) i ( n ) → 0 as n → ∞ where p ( n ) = j + 1 if j N n ≤ ( j + 1 ) N , j = 0 , 1 , 2 , … and n = j N + i ( n ) , i ( n ) ∈ { 1 , 2 , … , N } . Let F ≔ ⋂ i = 1 N F i x ( T i ) ≠ 0 and let f : H → H be a contraction mapping with coefficient α ∈ ( 0 , 1 ) , also let A be a strongly positive bounded linear operator with coefficient γ ¯ > 0 , and 0 γ γ ¯ α . Let { α n } , { β n } be sequences in ( 0 , 1 ) satisfying some conditions. Strong convergence of the implicit and explicit schemes are proved for a common fixed point of the family T 1 , T 2 , … , T n , which solves the variational inequality 〈 ( A − γ f ) x ¯ , x ¯ − x 〉 ≤ 0 ∀ x ∈ F . Our result generalizes and improves several recent results.

In this paper, we introduce a new iterative scheme by a hybrid method and prove a strong convergence theorem of a common element in the set of fixed points of a finite family of closed quasi-Bregman strictly pseudocontractive mappings and common solutions to a system of equilibrium problems in reflexive Banach space. Our results extend important recent results announced by many authors. MSC:47H09, 47J25.

Let E be a real Banach space and K be a nonempty, closed, and convex subset of E. Let be a finite family of Lipschitzian demi-contractive semigroups of K, with sequences of bounded measurable functions Li : [0, ∞) → (0, ∞) and bounded functions λi : [0, ∞) → (0, ∞), respectively, where , i = 1,2, ..., N. Strong convergence theorem for common fixed point for finite family is proved in a real Banch space. As an application, a new convergence theorem for finite family of Lipschitzian demi-contractive maps is also proved. Mathematics subject classification (2000) 47H09, 47J25

Let $E$ be a real $q$-uniformly smooth Banach space whose duality map is weakly sequentially continuous. Let $T:E\to E$ be a nonexpansive mapping with $F(T)\neq\emptyset.$ Let $A:E\to E$ be an $\eta$-strongly accretive map which is also $\kappa$-Lipschitzian. Let $f:E\to E$ be a contraction map with coefficient $0\lt \alpha\lt1.$ Let a sequence $\{y_{n}\}$ be defined iteratively by $y_{0}\in E,~~ y_{n+1}=\alpha_n\gamma f(y_n)+(I-\alpha_n\mu A)Ty_n,n\geq0,$ where $\{\alpha_n\},~~\gamma$ and $\mu$ satisfy some appropriate conditions. Then, we prove that $\{y_{n}\}$ converges strongly to the unique solution $x^{*} \in F(T)$ of the variational inequality $\langle(\gamma f-\mu A)x^{*},j(y-x^{*})\rangle\leq0,~\forall~y\in F(T).$ Convergence of the correspondent implicit scheme is also proved without the assumption that $E$ has weakly sequentially continuous duality map. Our results are applicable in $l_{p}$ spaces, $1\lt p \lt \infty$.

In this paper, we introduce a modified inertial subgradient extragradient algorithm in a 2-uniformly convex and uniformly smooth real Banach space and prove a strong convergence theorem for approximating a common solution of fixed point equation with a demigeneralized mapping and a variational inequality problem of a monotone and Lipschitz mapping. We present an example to validate our new findings. This work substantially improves and generalizes some well-known results in the literature.