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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.

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 main motivation of this paper is to present  the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

The authors establish a result concerning the L²-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.

The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.

In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

The paper aims to propose a practical model for market segment selection and evaluation. The paper carries out a technique of order preference similarity to the ideal solution (TOPSIS) approach to make an operation systematic dealing with multi-criteria decision- making problem.

Introducing a multi-criteria decision-making problem based on TOPSIS approach. A new entropy and new similarity measure under neutrosopic environment are proposed to evaluate the weights of criteria and the relative closeness coefficient in TOPSIS model.

The outcomes show that the TOPSIS model based on new entropy and similarity measure is effective for evaluation and selection market segment. Profitability, growth of the market, the likelihood of sustainable differential advantages are the most important insights of criteria.

This paper put forward an effective multi-criteria decision-making dealing with uncertain information.

This paper aims to propose a method of parametrizing topological transformer model at high flux densities in the core.

The approach proposed is based on terminal voltages and currents measured in a special purpose saturation test whose data are combined with typical saturation curves of grain-oriented electrical steels; the modeling is carried out in the ATPDraw program.

The authors corroborate experimentally the necessity of dividing the zero sequence impedance between all transformer phases and propose a method of the individual representation of the legs and yokes. This eliminates the use of nonexistent leakage inductances of primary and secondary windings.

The presented modeling approach can be used for predicting inrush current events and in the evaluation of the impact caused by geomagnetically induced currents (GICs).

The proposed approach is completely original and will contribute to a better understanding of the transients occurring in a transformer under abnormal conditions, such as inrush current events and GICs.

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.

In this work, the authors are interested in the notion of vector valued and set valued Pettis integrable pramarts. The notion of pramart is more general than that of martingale. Every martingale is a pramart, but the converse is not generally true.

In this work, the authors present several properties and convergence theorems for Pettis integrable pramarts with convex weakly compact values in a separable Banach space.

The existence of the conditional expectation of Pettis integrable mutifunctions indexed by bounded stopping times is provided. The authors prove the almost sure convergence in Mosco and linear topologies of Pettis integrable pramarts with values in (cwk(E)) the family of convex weakly compact subsets of a separable Banach space.

The purpose of the present paper is to present new properties and various new convergence results for convex weakly compact valued Pettis integrable pramarts in Banach space.