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Suppose C is any nonempty subset of a Banach space X. A mapping T : C → C is said to satisfy condition (Bγ,μ) if there exists μ ∈ [0, 1] and μ ∈ [0, 1/2 ] with 2μ ≤ γ such that for each two elements x, y ∈ C, γ||x - Tx|| ≤ ||x - y|| + μ||y - Ty|| implies ||Tx - Ty|| ≤ (1 - γ)||x - y|| + μ(||x - Ty|| + ||y - Tx||). In this research, we suggest some convergence results for these mappings under a up-to-date iterative process in a Banach space setting. Our results are new and improve some known results of the literature. [ABSTRACT FROM AUTHOR]

We compute the numerical solution of the Bratu's boundary value problem (BVP) on a Banach space setting. To do this, we embed a Green's function into a new two-step iteration scheme. After this, under some assumptions, we show that this new iterative scheme converges to a sought solution of the one-dimensional non-linear Bratu's BVP. Furthermore, we show that the suggested new iterative scheme is essentially weak w 2 -stable in this setting. We perform some numerical computations and compare our findings with some other iterative schemes of the literature. Numerical results show that our new approach is numerically highly accurate and stable with respect to different set of parameters. [ABSTRACT FROM AUTHOR]

The goal of this manuscript is to introduce the JK iterative scheme for the numerical reckoning of fixed points in generalized contraction mappings. Also, weak and strong convergence results are investigated under this scheme in the setting of Banach spaces. Moreover, two numerical examples are given to illustrate that the JK iterative scheme is more effective than some other iterative schemes in the literature. Ultimately, as an application, the JK iterative scheme is applied to solve a discrete composite functional differential equation of the Volterra-Stieljes type. [ABSTRACT FROM AUTHOR]

This manuscript is devoted to presenting some convergence results of a three-step iterative scheme under the Chatterjea–Suzuki–C ((CSC), for short) condition in the setting of a Banach space. Also, an example of mappings satisfying the (CSC) condition with a unique fixed point is provided. This example proves that the proposed scheme converges to a fixed point of a weak contraction faster than some known and leading schemes. Finally, our main results will be applied to find a solution to functional and fractional differential equations (FDEs) as an application. [ABSTRACT FROM AUTHOR]

The goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called (α,β,γ)-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the K-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the K-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the K-type iterative method to solve a variational inequality problem on a Hilbert space. [ABSTRACT FROM AUTHOR]

This paper introduces some numerical algorithms for finding solutions of nonlinear problems like functional equations, split feasibility problems (SFPs) and variational inequality problems (VIPs) in the setting of Hilbert and Banach spaces. Our approach is based on the Thakur-Thakur-Postolache (TTP) iterative algorithm and the class of mean nonexpansive mappings. First we provide some convergence results (including weak and strong convergence) in the setting of Banach space. To support these results, we provide a numerical example and prove that our TTP algorithm in this case converges faster to fixed point compared to other iterative algorithms of the literature. After that, we consider two new TTP type projection iterative algorithms to solve SFPs and VIPs on the Hilbert space setting. Our result are new in analysis and suggest new type effective numerical algorithms for finding approximate solutions of some nonlinear problems. [ABSTRACT FROM AUTHOR]

We consider the class of generalized α-nonexpansive mappings in a setting of Banach spaces. We prove existence of fixed point and convergence results for these mappings under the K∗-iterative process. The weak convergence is obtained with the help of Opial's property while strong convergence results are obtained under various assumptions. Finally, we construct two numerical examples and connect our K∗-iterative process with them. An application to solve a fractional differential equation (FDE) is also provided. It has been eventually shown that the K∗- iterative process of this example gives more accurate numerical results corresponding to some other iterative processes of the literature. The main outcome is new and improves some known results of the literature. [ABSTRACT FROM AUTHOR]

We give a multi-valued version of M iterative process [K. Ullah and M. Arshad, Numerical reckoning fixed points Suzuki's generalized nonexpansive mappings via new iteration process, Filomat 32 (2018) 187–196] in the setting of Banach spaces. After this, we prove some weak and strong convergence results for the class of multi-valued quasi-nonexpansive mappings (which contains the class of multi-valued nonexpansive mappings) with proper numerical examples using multi-valued version of M-iteration process. These results generalize several well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish several strong and weak convergence results for a class of mappings which is essentially wider than the class of Suzuki mappings using K iteration process in the context of uniformly convex Banach spaces. We also provide an example for support of our results. The obtained results are the extension and improvement of some recent results in the fixed point approximations theory. [ABSTRACT FROM AUTHOR]

We study the existence and approximation of fixed points for the recently introduced class of mappings called enriched Suzuki nonexpansive mappings in the setting of Banach spaces. We use the modified K-iteration process to establish the main results of the paper. The class of enriched Suzuki nonexpansive operators is an important class of nonlinear operators that includes properly the class of Suzuki nonexpansive operators as well as enriched nonexpansive operators. Various assumptions are imposed on the domain or on the operator to establish the main convergence theorems. Eventually, a numerical example of enriched Suzuki nonexpansive operators is used to show the effectiveness of the studied iteration scheme. The main outcome of the paper is new and essentially suggests a new direction for researchers who are working on fixed point problems in a Banach space setting. Our results improve and extend some main results due to Hussain et al. [ABSTRACT FROM AUTHOR]

In this paper, we prove some weak and strong convergence results for mappings satisfying condition (CC) using Ishikawa iteration process in uniformly convex Banach spaces. The results obtained in the paper extend and improve many well-known results in the iterations theory. [ABSTRACT FROM AUTHOR]

In this research, we suggest some convergence results for operators having (R C S C) condition in Banach space setting under F iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some appropriate assumptions on the domain or on the mapping. We furnish a non-trivial example of mappings having (R C S C) condition and show that its F iterative scheme is more effective than the corresponding well known iterative schemes on this particular example. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iteration process which is faster than the leading; S [J. Nonlinear Convex Anal. 8, no. 1 (2007), 61{79], Thakur et al. [App. Math. Comp. 275 (2016), 147{155] and M [Filomat 32, no. 1 (2018), 187{196] iterations for numerical reckoning fixed points. Using this new iteration process, some fixed point convergence results for generalized ff-nonexpansive mappings in the setting of uniformly convex Banach spaces are proved. At the end of paper, we offer a numerical example to compare the rate of convergence of the proposed iteration process with the leading iteration processes. [ABSTRACT FROM AUTHOR]

In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α -nonexpansive mappings. Secondly, by constructing an example of generalized α -nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature. [ABSTRACT FROM AUTHOR]

Let C be a nonempty subset of a Banach space X. A mapping T: C → C is said to satisfy(Bγ,μ) condition if there exists γ ∈ [0,1] and μ ∈ [0, ½] satisfying 2μ ≤ γ such that for each x,y ∈ C, γ||x-Tx||≤||x-y||+μ||y-Ty|| implies ||Tx-Ty||≤(1-γ)||x-y||+μ(||x-Ty||+||y-Tx||). In this paper, we obtain some convergence theorems for such mappings using M iterative process in uniformly convex Banach space setting. Our results extend and improve many results in the literature. [ABSTRACT FROM AUTHOR]

We connect the F iteration process with the class of generalized α -nonexpansive mappings. Under some appropriate assumption, we establish some weak and strong convergence theorems in Banach spaces. To show the numerical efficiency of our established results, we provide a new example of generalized α -nonexpansive mappings and show that its F iteration process is more efficient than many other iterative schemes. Our results are new and extend the corresponding known results of the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process. We also construct an example of mean nonexpansive mappings and show that it exceeds the class of nonexpansive mappings. To show the numerical accuracy of our main outcome, we show that Picard–Mann hybrid iteration process of this example is more effective than all of the Picard, Mann, and Ishikawa iterative processes. [ABSTRACT FROM AUTHOR]

This paper investigates fixed points of Reich-Suzuki-type nonexpansive mappings in the context of uniformly convex Banach spaces through an M ∗ iterative method. Under some appropriate situations, some strong and weak convergence theorems are established. To support our results, a new example of Reich-Suzuki-type nonexpansive mappings is presented which exceeds the class of Suzuki-type nonexpansive mappings. The presented results extend some recently announced results of current literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some weak and strong convergence results for generalized α -nonexpansive mappings using M iteration process in the framework of Banach spaces. This generalizes former results proved by Ullah and Arshad [Numerical reckoning fixed points for Suzuki's generalized nonexpansive mappings via new iteration process, Filomat 32(1) (2018) 187–196]. [ABSTRACT FROM AUTHOR]

Let K be a nonempty subset of a Banach space E. A mapping T : K → K is said to satisfy (RCSC) condition if each a , b ∈ K , 1 / 2 a − F a ≤ a − b ⇒ F a − F b ≤ 1 / 3 a − b + a − F b + b − F a . In this paper, we study, under some appropriate conditions, weak and strong convergence for this class of maps through M iterates in uniformly convex Banach space. We also present a new example of mappings with condition (RCSC). We connect M iteration and other well-known processes with this example to show the numerical efficiency of our results. The presented results improve and extend the corresponding results of the literature. [ABSTRACT FROM AUTHOR]

In this article, we prove some weak and strong convergence theorems for mappings satisfying condition (E) using the A K iterative scheme in the setting of Banach spaces. We offer a new example of mapping with condition (E) in support of our main result. Our results extend and improve many well-known corresponding results of the current literature. [ABSTRACT FROM AUTHOR]

In this article, we introduce a novel iterative algorithm to approximate fixed point of mappings with B γ , μ condition. We establish some strong and weak convergence results in a uniformly convex Banach space. Using a numerical example, we compare the speed of the proposed algorithm with some leading iterative algorithms. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the modified Agarwal-O'Regan-Sahu iteration process (S-iteration) for finding endpoints of multivalued nonexpansive mappings in the setting of Banach spaces. Under suitable conditions, some weak and strong convergence results of the iterative sequence generated by the proposed process are proved. Our results especially improve and unify some recent results of Panyanak (J. Fixed Point Theory Appl. (2018)). At the end of the paper, we offer an example to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper we propose a new iteration process, called AK iteration process, for approximation of fixed points for contraction mappings. We show that our iteration process is faster than the leading Vatan Two-step iteration process for contraction mappings. Numerical examples are given to support the analytic proofs. Stability of AK iteration process and data dependence result for contraction mappings by employing AK iteration process are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we provide and study the concept of multi-valued generalized (α , β) -nonexpansive mappings, which is the multi-valued version of the recently developed generalized (α , β) -nonexpansive mappings. We establish some elementary properties and fixed point existence results for these mappings. Moreover, a multi-valued version of the M-iterative scheme is proposed for approximating fixed points of these mappings in the weak and strong senses. Using an example, we also show that M-iterative scheme converges faster as compared to many other schemes for this class of mappings. [ABSTRACT FROM AUTHOR]

In this article, the recently introduced iterative scheme of Hassan et al. (Math. Probl. Eng. 2020) is re-analyzed with the connection of Reich–Suzuki type nonexpansive (RSTN) maps. Under mild conditions, some important weak and strong convergence results in the context of uniformly convex Banach spaces are provided. To support the main outcome of the paper, we provide a numerical example and show that this example properly exceeds the class of Suzuki type nonexpansive (STN) maps. It has been shown that the Hassan et al. iterative scheme of this example is more useful than the many other iterative schemes. We provide an application of our main results to solve split feasibility problems in the setting of RSTN maps. The presented outcome is new and compliments the corresponding results of the current literature. [ABSTRACT FROM AUTHOR]

The purpose of this research work is to prove some weak and strong convergence results for maps satisfying (E)-condition through three-step Thakur (J. Inequal. Appl.2014, 2014:328.) iterative process in Banach spaces. We also present a new example of maps satisfying (E)-condition, and prove that its three-step Thakur iterative process is more efficient than the other well-known three-step iterative processes. At the end of the paper, we apply our results for finding solutions of split feasibility problems. The presented research work updates some of the results of the current literature. [ABSTRACT FROM AUTHOR]

We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized α -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms. [ABSTRACT FROM AUTHOR]