This paper provides iterative solutions, via some variants of the extragradient approximants, associated with the pseudomonotone equilibrium problem (EP) and the fixed point problem (FPP) for a finite family of $ \eta $-demimetric operators in Hilbert spaces. The classical extragradient algorithm is embedded with the inertial extrapolation technique, the parallel hybrid projection technique and the Halpern iterative methods for the variants. The analysis of the approximants is performed under suitable set of constraints and supported with an appropriate numerical experiment for the viability of the approximants.

The aim of this paper is to find out fixed point results with interpolative contractive conditions for pairs of generalized locally dominated mappings on closed balls in ordered dislocated metric spaces. We have explained our main result with an example. Our results generalize the result of Karapınar et al. (Symmetry 2018, 11, 8).

To solve the problems of curves and surfaces approximation with normalized totally positive bases, a new progressive and iterative approximation for least square fitting method called HSS-LSPIA is proposed, which is based on the HSS iterative approach for solving linear equations of LSPIA. The HSS-LSPIA format includes two iterations with iterative difference vectors, each of which is distinct from the other. The approximate optimal positive constant, as well as convergence analyses, are provided. Furthermore, the HSS-LSPIA method can be faster than the ELSPIA, LSPIA, and WHPIA methods in terms of convergence speed. Numerical results verify this phenomenon.

In the current note, we broaden the utilization of a new and efficient analytical computational scheme, approximate analytical method for obtaining the solutions of fractional-order Fokker-Planck equations. The approximate solution is obtained by decomposition technique along with the property of Riemann-Liouuille fractional partial integral operator. The Caputo-Riemann operator property for fractional-order partial differential equations is calculated through the utilization of the provided initial source. This analytical scheme generates the series form solution which is fast convergent to the exact solutions. The obtained results have shown that the new technique for analytical solutions is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology.