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Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and △-convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT(0) spaces and Hilbert spaces as special cases.

In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.

Showed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued ρ-quasi-contractive mappings in modular function spaces. We approximate fixed points of this class of nonlinear multivalued mappings in modular function spaces. Moreover, we extend the concepts of T-stability, almost T-stability and summably almost T-stability to modular function spaces and give some results.

In this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to converge to the fixed point of a multivalued map T such that PρT, an associate multivalued map, is a ρ-contractive-like mapping.

The concepts of relative ρ-stability and weak ρ-stability are introduced, and conditions in which these multistep iterations are relatively ρ-stable, weakly ρ-stable and ρ-stable are established for the newly introduced strong ρ-quasi-contractive-like class of maps.

Noor type, Ishikawa type and Mann type iterative sequences are deduced as corollaries in this study.

The results obtained in this work are complementary to those proved in normed and metric spaces in the literature.

This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.

The results of this paper are theoretical and analytical in nature.

The authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.

Analytical and theoretical results.

The results of this paper can be applied in science and engineering.

The results of this paper is applicable in certain social sciences.

The results of this paper are new and will open up new areas of research in mathematical sciences.

The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.

The results of this paper are theoretical and analytical in nature.

The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.

The results are theoretical and analytical.

The results were applied to solving nonlinear integral equations.

The results has several social applications.

The results of this paper are new.

The purpose of the paper is to describe ambidextrous learning in organizations within the customer order-based context (COBC), here based on a dynamic view of work processes. The study focuses on how organizations can learn while working with customer orders, considering learning in organizations as both a process and an outcome.

This conceptual article focuses on learning in the COBC, where the individual customer requirements represent a key input into the organization’s work processes, thus limiting the possibilities to plan and standardize. The COBC brings about challenges and potentials for learning in organizations where task variety and complexity are high and in which the contradictory interplay between efficiency and responsiveness is apparent not only at a strategic level but also at an operative level in the customer order fulfillment processes. Depending on the variations in tasks and parallel complex work processes between different units in the organization, the ambidextrous learning dynamic can appear in the COBC.

Five propositions were made from the analysis: Proposition 1: Learning in the COBC can occur both in real-time but also in retrospect and with sporadic and recurrent interventions. Proposition 2: Learning in the COBC can occur for, as well as from, customer order processes. Proposition 3: Learning in the COBC varies and will depend on the delivery strategy. Proposition 4: Learning can be stimulated by the variation in priorities among customer orders in the COBC because the work characteristics for the back office and front office differ between customer order fulfillment processes. Proposition 5: Learning in the COBC can occur both within the back office and front office but also between these organizational units. The paper discusses the importance of building learning infrastructure in COBC and how that can be supported by a suggested learning office.

The present study demonstrates the importance of functions being able to act both as back office and front office in relation to delivery strategy. It also shows the ambidextrous learning process for the sake of improving both the internal efficiency and external effectiveness across the organization.