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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.

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.

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 purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

The purpose of this paper is to apply the quantum “eigenlogic” formulation to behavioural analysis. Agents, represented by Braitenberg vehicles, are investigated in the context of the quantum robot paradigm. The agents are processed through quantum logical gates with fuzzy and multivalued inputs; this permits to enlarge the behavioural possibilities and the associated decisions for these simple vehicles.

In eigenlogic, the eigenvalues of the observables are the truth values and the associated eigenvectors are the logical interpretations of the propositional system. Logical observables belong to families of commuting observables for binary logic and many-valued logic. By extension, a fuzzy logic interpretation is proposed by using vectors outside the eigensystem of the logical connective observables. The fuzzy membership function is calculated by the quantum mean value (Born rule) of the logical projection operators and is associated to a quantum probability. The methodology of this paper is based on quantum measurement theory.

Fuzziness arises naturally when considering systems described by state vectors not in the considered logical eigensystem. These states correspond to incompatible and complementary systems outside the realm of classical logic. Considering these states allows the detection of new Braitenberg vehicle behaviours related to identified emotions; these are linked to quantum-like effects.

The method does not deal at this stage with first-order logic and is limited to different families of commuting logical observables. An extension to families of logical non-commuting operators associated to predicate quantifiers could profit of the “quantum advantage” due to effects such as superposition, parallelism, non-commutativity and entanglement. This direction of research has a variety of applications, including robotics.

The goal of this research is to show the multiplicity of behaviours obtained by using fuzzy logic along with quantum logical gates in the control of simple Braitenberg vehicle agents. By changing and combining different quantum control gates, one can tune small changes in the vehicle’s behaviour and hence get specific features around the main basic robot’s emotions.

New mathematical formulation for propositional logic based on linear algebra. This methodology demonstrates the potentiality of this formalism for behavioural agent models (quantum robots).

The aim of this paper, using the intuitionistic fuzzy (IF)–set based Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method, is to create multicriteria decision-making (MCDM) mechanism that evaluates the papers according to the offset print quality, separately for each of the CMYK colors. Thanks to the mechanism, the most suitable and the most unsuitable paper for printing is determined.

With the IF PROMETHEE method, respectively, deviations are calculated by linear criteria type; the overall IF preference relation matrix is obtained. Finally, the positive and negative outranking flows are calculated; by obtaining net outranking flows, all papers are ranked from best to worst for printability.

Based on the results of the MCDM algorithm; the best offset printing quality is Matte Coated 115 gr. for cyan, magenta and black and Glossy Coated 115 gr. for yellow. The worst offset printing quality for all papers is 70 gr. III. low grade paper. According to the findings, when all colors are examined, the best paper for offset printing quality is coated papers; the worst paper is III. low grade papers.

The creation of mechanism that evaluates all criteria together leads to the most accurate result. Cases of hesitation are also addressed using an IF-based algorithm; all criteria were assigned individual importance levels, and a single result was obtained by activating all of the criteria simultaneously. Therefore reasons, this is paper that will bring innovation and shed light on studies in this field.

The paper seeks to develop dual 3D finite element (FE) formulations for modeling both inductive and capacitive effects in massive inductors, in particular micro‐coils. The paper aims to build circuit relations relating the voltages and the currents in such inductors to be used in circuit coupling.

A circuit relation involving a unique voltage and complementary inductive and capacitive currents is defined for each inductor. The inductive circuit relation is first classically obtained by a FE magnetodynamic model. Then, the capacitive relation is obtained through a FE electric model, using sources evaluated from the first model. The conformity is defined on one hand for the magnetic flux density and the electric field, and on the other hand for the magnetic field and the electric flux density. Mixed FE, i.e. nodal, edge and face elements, are used to satisfy each chosen conformity level for the unknown fields and to naturally define the involved global quantities, i.e. the voltages, currents and charges.

This contribution points out the interest of satisfying conformity properties for the coupled magnetic and electric problems. An accurate computation of these effects is obtained in the critical frequency range of their strong interaction. In addition, the complementarity of dual solutions gives the possibility to estimate the discretisation error.

The mathematical and discretisation tools for any wished conformity level are unified for naturally coupling magnetic and electric problems. The global quantities basis functions involved in the FE circuit relations benefit from a significant support reduction, which facilitates their evaluation and gives them direct physical interpretations.

Two variational formulations of the three‐dimensional eddy‐current problem are discussed and compared. One is based on the use of h (the magnetic field) and the associated magnetic potential as unknowns the other one is based on the use of a primitive of the electric field. They are found to be quite similar, suggesting some “duality” and, perhaps more importantly, that “mixed” finite elements, which were found efficient for the first case, could also be used for the second. This could alleviate some problems with the so‐called “modified vector potential approach” to the 3‐D eddy‐current problem.